Reference no: EM132573767

Microeconomic Theory Assignment - University of Massachusetts Boston

Q1. Determine the utility function (equation) that describes each of the following set of indifference curves:

Q2. Sketch indifference curve for the given utility levels. Describe in a sentence or two the consumer's preferences for the two goods.

U(x, y) = 2y; U = 10

U(x, y) = x+y; U = 10

U(x, y) = min(x, y); U = 10

U(x, y) = x-y; U = 10

Q3. Mohammed loves hamburgers and beer but when given the choice between two bundles of burgers and beer he will always prefer the bundle with more hamburgers no matter how many beers each contain. If the bundles nave equal burgers he will then choose the bundle with more beer,

Diagram Mohammed's preferences.

What is Mohammed's demand function for Hamburgers?

Q4. Ali spends his income of $64 on kerosene (k) and food (f) each week. The price of food is $8 per unit and the price of kerosene is $4 per liter. His utility function is U(k, f) = kf³; MUk = f³ and MUf = 3kf².

What is Ali's optimal bundle?

If the price of food increases to $10 determine the substitution and Income effects using the Hicksian method.

Q5. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers.

q = [min (K, 2L)}²

q = x min(x, y)

Q6. Draw the isoquant for the following production function and indicated level of output.

Q = min (2L, 0.5L + 0.5K, K) Q = 4

Q7. An Italian sausage maker's production function is Q = 8K^.25L^.75MPk = 2K^-.75L^.75, MPI = 6K^.25L^-.25

Determine the firm's short-run cost equation (assume K is the fixed input).

Determine the firm's long-run cost equation.

If the price of K is $4 and the price of L is $24 and K is fixed at 32 units determine the K, L, q where the short-run cost equals the Iona-run cost. What is the cost?

Q8. Primo Fungi, a mushroom firm desires to produce 125 crates of Portobello mushrooms in the least costly manner. The firm's production function is Q = K² + L² MPk = 2K, MPL = 2L. The price of K is $4 and the price of L is $2.

Determine the optimal K, L combination.

What is the associated cost?

Q9. In Takeout Town, there are 45 identical pizza delivery firms, each firm having the cost function c(q) = 0.5q²+4q+162 where q is the quantity or pizzas produced by a typical firm. The market demand function is Q^d = 820-5p.

Find a firm's individual supply curve.

Find the market supply curve.

Determine the equilibrium P and Q.

Calculate the individual firm's q and π.

Q10. The utilities commission in a city is currently examining pay internet service in the city. The commission has been asked to evaluate a proposal by a city council member to place a $.10 price ceiling on the service. The staff economist at the utilities commission estimates the demand and supply curves for Internet Service as follows:

Qd = 1600 - 2400P

Qs = 200 + 3200P

Determine the equilibrium price and quantity that will prevail without the price celling.

What is the quantity that will be available with the price celling?

Determine the "dead-weight" loss due to the ceiling.

Q11. Hawkins Micro Brewery has a monopoly on Oatmeal Stout in the local market. The inverse demand is P = 50-.5Q. The marginal revenue is MR = 50- 1Q. MC = 5+.5Q.

Calculate Hawkins profit maximizing output.

Calculate the producer surplus.

Calculate the dead-weight loss.

What is the optimal price ceiling?

If Hawkins was able to practice perfect price discrimination what price would it charge?

What is the new producer surplus?