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Questions and Answers of Microeconomics

Solve Exercise E3 assuming additionally that resources of production factorsExercise E3There are given: are limited: Vi = 1, 2 0xi bi, where Vi= 1, 2 bi > 0 means the constrained resource of i-th
Solve Exercise E3 taking simultaneously into account the data from Exercises E4 and E5.Exercise E3There are given:Exercises E4Solve Exercise E3, when the production total cost function has a
There are given: X = (X1, x) (0, 0)-a vector of inputs of production factors, y = f(x)-an output level described by an increasing, strictly concave and twice differentiable production function, (#)
Solve Exercise E7, when the production total cost function has a form:Exercise E7There are given: or equivalently: clot (x1, x2) = a(f(x, x)) + (x, x) + Y, tot (y) =ay +By+y, where y=f(x1, x2) is an
Solve Exercise E7 assuming additionally that resources of production factors Exercise E7There are given: are limited: Vi = 1, 2 0xi bi, where Vi= 1, 2 bi > 0 means the constrained resource of i-th
Solve Exercise E7 taking simultaneously into account the data from Exercises E8 and E9.Exercise E7There are given:Exercise E8Solve Exercise E7, when the production total cost function has a
A production process in some firm acting in the perfect competition is described by a one-variable production function of a form: f (x(t)) = x (t) 0.25 In periods t = 0, 1, 2, ..., 20 the price of a
At any moment t = [0;20] a firm and conditions in which it acts are described as in Exercise E11, except additional constraint in a form of a production factor resource:Exercise E11A production
A production process in a firm acting as a monopoly is described by a one- variable production function of a form: f(x(t)) = x (t) 0.25 The price of a product manufactured by this monopoly changes
At any moment a monopoly and conditions in which it acts are described as in Exercise E13, except for an additional constraint in a form of a production factor resource:Exercise E13A production
What are a demand function and an inverse function of demand for one product?
What conditions need to be satisfied by exogenous linear: demand function and function of product supply to have a positive equilibrium price established on a market of this product?
How the optimal supplies by each of two producers and the optimal total supply react to changes in values of parameters of production cost functions and demand function when both producers act in
What are the relationships between a product price set by a monopolist and price elasticity of demand for this product?
How do the optimal supply and a product optimal price set by a monopo- list react to changes in values of parameters of production cost function and demand function when there is an exogenously
What is meant by discriminatory pricing practised by a monopolist for one product intended for two independent markets of the same product?
What are the conditions by which prices of one product supplied by a monopolist for two different markets are equal?
What are the conditions that should be satisfied by functions of demand for product in the Cournot, Stackelberg and Bertrand duopoly models?
How do firms acting on markets described by Cournot, Stackelberg and Bertrand duopoly models decide on their strategies of rational behaviour?
When do producers acting on a duopolistic market decide to compete on quantities of supplied product and when on prices?
What does it mean that two producers have equal positions on a duopolistic market and that one is a leader and the other is a follower?
What are the mechanisms of reaching an equilibrium state in the Cournot, Stackelberg and Bertrand duopoly models?
What conclusions can be drawn on the basis of comparative analysis of equi- librium states on a market of one product in case of pure monopoly, Cournot and Stackelberg duopoly models?
Determine an inverse function of demand and a function inverse to a given demand function: yd (p) = -apa + b, a, b > 0. Draw graphs of these functions in the case when: (a) a (0, 1), (b) a > 1.
There is a market for a product with exogenously determined demand function and product supply function: (a) ya (p) = -ap + b, a, b>0, ys (p) = cp +d, c, d > 0, b>d, (b) ya (p) = ap + b, a,b>0, y (p)
Three producers act in perfect competition on a market of one homogenous product. A function of demand for the product is linear yd (p) = ap+b, a, b > 0, functions of production total costs are also
Formulate and solve a problem of choice of the optimal supply and of the optimal price set by a monopolistic company considered in Example 5.3. Assume a nonlinear function of production total cost of
Consider the Cournot duopoly model when a production total cost function for i-th producer (i = 1, 2) is nonlinear and of a form: 0. Determine optimal levels of: the product supply by each
Two producers act on a market of two heterogeneous substitute products. The first producer (leader) can set an optimal price of her/his product on a level that guarantees her/him the maximum profit
Compare the original and the modified Bertrand duopoly models. State if the leader position in the modified Bertrand duopoly model is more beneficial for the first producer than a market position
The demand for a product of a monopolistic company evolves according to a linear function of a form: yd (t) = a(t)p(t) + b(t), a(t), b(t) > 0, A function of production total cost is given as ko (ys
Some monopolistic company considers discriminatory pricing for its product supplied to two different markets. The demand reported by consumers for i-th product (i = 1, 2) evolves according to a
Two producers having equal positions act on a market of some homogeneous product. The demand for this product evolves according to a demand function: yd (p) = -ap+b, a, b > 0.
Two producers act on a market of some homogeneous product. The first of them has a position of the leader and the other a position of the follower. The demand for this product evolves according to a
Two producers having equal positions on a market offer two substitute products. The demand for these products evolves according to the following demand functions: y (P, P2) = ap +2 +, y (P, P2)=a2p2
Two producers having equal positions on a market offer two substitute prod- ucts. The demand for these products evolves according to the following demand functions: y (P, P2) = ap +2 +, == y (P1,
Explain why an excess demand function, in the discussed model of a market of a single good with exogenously determined functions of supply and demand, is positively homogenous of degree 0 and
Present analytical forms of functions of the demand and of the supply on a market of two goods so that these goods are (a) independent, (b) complementary, (c) substitute, to each other.
Proceeding with the answer to question 2 state if each of these three cases: independency, substitutability, or complementarity makes economic sense in the considered model.Question 2Present
Justify that in the static Arrow-Debreu-McKenzie model vector functions of the demand and of the supply are determined endogenously.
What are the basic differences between the static Arrow-Debreu-McKenzie model and the static model of a market of two goods with exogenous functions of the supply and of the demand?
What is the difference between the Walrasian equilibrium state and Walras's law in the static Arrow-Debreu-McKenzie model?
What is the difference between the Walrasian equilibrium allocation and the Pareto optimal (efficient) allocation in the static Arrow-Debreu-McKenzie model?
How is a feasible trajectory of prices in the dynamic Arrow-Debreu-McKenzie model defined in its discrete-time or continuous-time version?
What is the significance of feasibility of a trajectory of goods' prices for its asymptotic convergence to the equilibrium state in the dynamic Arrow- Debreu-McKenzie model in the discrete-time or
What does it mean that the Walrasian equilibrium price vector in the dynamic Arrow- Debreu-McKenzie model, in the discrete-time or continuous-time version, is asymptotically globally stable?
There is a market of a homogeneous product with exogenously determined demand function: yd (p) cp +d, c, d >0. = -apa + b, a, b > 0 and supply function: ys (p) = 1. For a product price, the demand
There is given a market of two products with exogenous demand functions: y (p) = ap + v P2 + b, y (p) = - a2 p2 + y2P + b, ai, bi, Vi > 0, i = 1,2 and exogenous supply functions: yi (p) =cipi +81 P2
Present the model of a market of a single good from Exercise E1 as (a) a dynamic discrete-time model, (b) a dynamic continuous-time model.Exercise E1There is a market of a homogeneous product with
Present the model of a market of two goods from Exercise E2 as (a) a dynamic discrete-time model, (b) a dynamic continuous-time model.Exercise E2There is given a market of two products with exogenous
An owner of a strawberry plantation hires one worker who has 24 units of time. The employee can allocate part of the time to work and part to rest. He/she owns 20% of shares in profits of the
Consider a discrete-time version of the dynamic Arrow-Debreu-McKenzie model for the same data given as in Exercise E5. Initial prices are:Exercise E5An owner of a strawberry plantation hires one
Consider a continuous-time version of the dynamic Arrow-Debreu-McKenzie model for the same data given as in Exercise E5.Exercise E5An owner of a strawberry plantation hires one worker who has 24
What does it mean that a utility function is a numerical characteristics of a relation of consumer’s preference?
What are first and second Gossen’s laws? What properties are required for a utility function to have any of these laws satisfied?
Why does a linear utility function describe goods that are perfect substitutes and not complementary to each other? Why does a Koopmans-Leontief utilityfunction describe goods that are perfect
What is a difference between a Giffen good and a Veblen good?
What are criteria to classify consumer goods and what is economic interpre-tation of these criteria?
What are basic properties of a Marshallian demand function and of an indirect utility function?
What are basic properties of a Hicksian demand function and of a consumer’s expenditure function?
Why a Hicksian demand function is also called a compensated demand function?
Regarding a consumption utility maximization problem what assumptions are needed to have a marginal utility of a money unit for the purchase of i-th good equal to a marginal utility of a consumer’s
What is Roy’s identity in a consumption utility maximization problem? What is the counterpart of this identity in a consumer’s expenditure minimization problem?
What conditions need to be satisfied to have a Hicksian demand function and a Marshallian demand function having the same values?
What assumptions should be satisfied to derive a Slutsky equation?
What conclusions can be drawn from a Slutsky equation?

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