Task 03.

Kindly show steps and calculations clearly!

The demand curve for pizza in the Smalltown is: Qd = 120 - P, where Qd represents the quantity demanded of pizza in the Smalltown, and P represents the market price of pizza.

There are TWO pizza restaurants in Smalltown now: Restaurant A and Restaurant B. Both of them have the same cost of production, that is Restaurant A's total cost of production is TCA= 600 + 24qA , and Restaurant B's total cost of production is: TCB= 600 + 24qB, where qA and qB are the output level chosen by Restaurant A and B, respectively. Restaurant A and B strategically interact with each other.

a) If Restaurant A and B enter into a collusion agreement and split the market, what will be the market (total) equilibrium quantity and market equilibrium price? (4 points)

b) If Restaurant A and B choose their output (quantity produced) to maximise profit, do you think that they will both honor their collusion agreement? What are the levels of output for each restaurant and the market equilibrium price? Please explain with equations/models and your reasoning clearly. (8 points)

c) If Restaurant A and B get into a competition by choosing their price level, what will be the equilibrium market price and equilibrium market quantity? (2 points)

d) Given the answer from part c), what will be the possible problem(s) facing by Restaurant A and B? (4 points)

e) Given the market demand and cost function stay the same as above, and if the number of restaurants increases to 5. If restaurants compete by choosing quantity produced, what will be the equilibrium market (total) quantity and price? (4 points)

Now, let the market demand curve: Qd = a - bP ("a" and "b" are the unknown parameter); the number of restaurants increases to 3 (Restaurant A, B, and C) and Restaurant A's cost function is: TCA= FA + cAqA; Restaurant B's cost function is: TCB= FB + cBqB; Restaurant B's cost function is: TCC= FC + cCqC, where FA, cA, FB, cB, FC, cC are all positive numbers.

f) Please find the best response function of Restaurant A, B, and C in general form, respectively. *Here, only the best response function of Restaurant A, B, and C would be enough, you don't need to solve the equilibrium. (10 points)

Two.

Exercise 1 - Slutsky equation

1. Assume there are two goods, 1 and 2. Illustrate graphically the Slutsky decomposition of a decrease in the price of good 1 under the assumption that it is a normal good.

2. Assume there are two goods, 1 and2 Illustrate graphically the Hicks decomposition of an increase in the price of good 1 under the assumption that it is an inferior good (but not Giffen). Write down the Slutsky equation for good 1 and give a sign to the income, substitution and total effects.

3. Given that good 1 is inferior, can good 2 also be inferior? (Hint: consider the budget constraint at the optimal consumption point of the utility-maximisation problem, and take the derivative with respect to budget y.)

4. In Exercise 2 from PS3, which pairs of goods would you regard as substitutes and which as complements?

5. In Exercise 2 from PS3, compute the total effect, the income effect and the compensated effect of an own-price change for good 1. Is the Slutsky equation satisfied? Justify your results.

Question: Exercise 2 - Consumer demand with non-linear budger sets Consumers live on bread x and cheese y. ...

Exercise 2 - Consumer demand with non-linear budger sets Consumers live on bread x and cheese y. They face the following pricing schedule. If consumption is below A loaves of bread then each loaf costs $1. If consumption is A or more then the price falls to $ 1 2 (on every loaf and not just those in excess of A). The price of cheese is $1 per unit, regardless of the amount consumed.

1. What is the maximum amount of cheese a consumer with a total budget of M can afford if she buys less than A loaves of bread? And if she buys A or more loaves?

2. Draw the budget constraint for someone with total budget of $10, labelling all relevant slopes and intercepts. Is the budget set convex? Justify your answer.

3. Raul has preferences represented by the function uR(x, y) = min[x; y] and a total budget of $10.

(a) How many loaves would he buy if he paid a constant price of 1 for every loaf of bread, regardless of the total amount of break purchased? (Hint: Draw Raul's indifference map. Then argue that he will optimally choose to consume equal quantities of cheese as bread: x = y .)

(b) How many loaves would he buy if he paid a constant price of 1/ 2 for every loaf of bread, regardless of the total amount of break purchased? (Hint: follow the same line of argument as in the previous question.)

(c) Hence determine how many loaves Raul will buy subject to the nonlinear constraint described in (2.) if A = 5.

4. Now consider Gabriela with the same budget as Raul, but preferences uG(x, y) = min[2x; y]. How does her demand differ from Raul's when facing the nonlinear constraint described in (2.) if A = 5? Give an intuition for this result.