Please help me understand the following questions.

Question 1 There are 10,000 identical individuals in the market for commodity X, each with a demand function given by Qodx = 12 - 2Px, and 1000 identical producers of commodity X, each with a function given by Qsx = 20 Px. where Qox is an individual's quantity demanded, Qsx is a single producer's quantity supplied, and Px is the price of the commodity. (a) Find the market demand function (QDx) and the market supply function (QSx) for commodity X (b) Determine the market demand schedule and the market supply schedule of commodity X (for whole dollar prices) and from them find the equilibrium price and the equilibrium quantity. (c) Plot, on one set of axes, the market demand curve and the market supply curve for commodity X and show the equilibrium point (d) Obtain the equilibrium price and the equilibrium quantity mathematically. (e) Explain why the equilibrium condition is considered stable. (f) Determine the elasticity of demand for commodity X at the equilibrium point. Question 2 Suppose that from the condition of equilibrium in Question 1, there is an increase in consumers' incomes (ceteris paribus) so that a new market demand curve is given by QDx = 140,000 - 20,000Px. (a) Derive the new market demand schedule (b) Show the new market demand curve on the graph used in Question 1(c) (c) State the new equilibrium price and equilibrium quantity for commodity X (d) Determine the Income Elasticity at the original equilibrium price and at the new equilibrium price. (Assume that the increase in income is 106). (e) In the light of your answer to 2 (d), comment on the nature of commodity X.(3) You and a classmate are assigned a project on which you will receive one combined grade. You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation: If you both work hard, you get an A, which gives you each 40 units of happiness .If only one of you works hard, you both get a B, which gives you each 30 units of happiness. .If neither of you works hard, you both get a D, which gives each of you 10 units of happiness. . Working hard costs 25 units of happiness. (a) Fill in the following payoff matrix: Your decision Work Shirk Classmate's Work decision Shirk (b) What is the likely outcome? Explain your answer. T (c) If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)?ocew/content/group/1:406fble 2593-423d-bf71-710356373a56/Problem?120sets/Lcon101P57.pdf of quantity. Then find marginal revenue as the derivative of total revenue with respect to quantity. Plot MR, and explain why it is downward sloping- (e) The monopolist's optimal quantity occurs where MC crosses MR. Mark this quantity on the graph, and make sure it matches your answer to 2(d)- (f) Also mark the monopolist's price Pm from 2(e). Is this price above or bekes ATC at that quantity? Explain why you knew that would be the case. (g) The competitive market outcome happens when the demand function crosses marginal cost (the supply function in a competitive market). Find p" and y" as if the market were competitive. Mark these on the graph. 4. This question concerns surplus and efficiency of the market under monopoly. (a) On the graph you just drew, shade/color (and label) the areas corresponding to producer and consumer surplus under the monopoly outcome. (b) Calculate consumer and producer surplus. Note that producer surplus is a trapezoid; you can calculate its area either by splitting it into a rectangle and a triangle, or by using the formula for the area of a trapezoid (Google it if you don't know). (e) Recall that producer surplus is profit plus fixed cost. Is that the case here? (d) On the graph you drew in question 2, shade/color (and label) the area that represents the deadweight loss from having the monopolist outcome (Pa. ym) rather than the com- petitive outcome (p' y') then calculate its value. 842. In class, we've discussed the fact that the baseline models we've constructed can be extended to incorporate more advanced techniques. Let's look at a specic extension that incorporates the concept of price discrimination. In particular, assume that a rm with constant marginal cost of $2 (and no xed cost) has two types of customers The rst type has a market demand of 01 (p) = 30 p. The second type is more price sensitive and has a market demand of D2 (p) = 30 2p. A. Assume the rm can only set a single price. For instance, when an individual shows up to purchase a good, the rm cannot determine which type of consumer she is. What is the maximal prot the rm can achieve. HINT: This is pretty much a standard market power model where you need to solve for the market demand, prot maximize, then determine if the rm would sell to each customer. B. Now, assume the rm can set a different price in each market. For instance, the rm can offer senior citizen discounts. If the rm prot maximizes in market 1 and also market 2, what prices will be set in each market? C. How much extra prot will the rm receive by price discriminating (i.e., setting a different price in each market)