ECONOMICS S-1010

SUMMER 2020

SUMMER SCHOOL

MICROECONOMICS • MIDTERM EXAMINATION (GRADUATE)

You have 120 minutes to finish the exam.

Closed books & notes, but calculator allowed.

You should spend about 25 minutes on each question,

so that you have time to re-check.

Show all calculations, explain all answers, fully label graphs,

and highlight all final answers.

1. Theory of the Consumer:

Maya divides her $1,500 income between the consumption of food (X) and all else (Y).

Her preferences can be described by the following utility function: U = X2 Y.

When the price of food is $4 and of all else is $10, she chooses the bundle (250, 50).

a) If now the price of food rises to $5, how much of each good will she choose? 6

b) Explain this change in terms of income and substitution effects. 6

c) How much would she be willing to pay to avoid this price increase? 6

d) Derive her demand curve for food, her income expansion path and Engel curve (when food costs $5). 7

2. Theory of the Firm:

a) Short answers (write 2-3 lines only per question):

(i) Why is the Lagrange method useful in solving constrained optimization problems?

(ii) What is the economic relevance of the Lagrangian multiplier?

(iii) What is the dual of a problem, and why is it useful?

(iv) What is the dual of: L = wL + rK – λ (A Kα Lβ – Q)? 10

b) Derive the elasticity of substitution along a Cobb-Douglas production function. 8

c) If we have data on costs (C), input prices (w, r) and output (Q), how can we estimate the Cobb-Douglas production function (give an outline only)? Why is this important? 7

3. Perfect Competition:

A firm in a perfectly competitive industry has this cost function: TC = 1000 + 10q2 .

a) If market demand is QD = 3000 – 10P, what is the long-run equilibrium price, quantity produced by the firm and the industry, the number of firms in the industry, and profit? 8

b) If demand increases by 1000 for all Q, what changes in the short-run? Now, what changes in the long-run? 12

c) If costs were to double, how would price, firm and industry quantity, number of firms, and profit change, in the short-run and long-run? (Answer briefy and qualitatively – i.e. without any calculations. Use your intuition!) 5

4. Short Run Demand Curve for Labor:

a) Explain to a layperson (i.e. in purely non-economic terms) what one should be paid (in equilibrium)? Now, state this as an equation using economic terms. 9

b) Draw the general short run labor demand curve, clearly labeling the axes and curves. 8

c) A firm has a short-run production function defined by: Q = –0.05L2 + 10L. What is the short run demand curve for labor (L) in terms of the market wage rate (w), if the firm can sell all its output at $10 per unit? 8

5. Are each of the following assertions TRUE, FALSE, or UNCERTAIN?

Explain your answers, using graphs where possible.

a) Bob’s optimal consumption bundle is (X*, Y*). A year later, his income and the prices of X and Y have all changed, but his new budget line (with new slope) still goes through (X*, Y*). This means he is just as well off as before and should consume the same bundle. (Assume the standard consumer theory model as discussed in class.) 9

b) The firm’s short-run demand curve for labor is the same as its marginal revenue product of labor curve. 8

c) If there are many (> 2) factors of production (inputs), the optimal combination of these is where their marginal products are the same. 8

6. These questions are unrelated.

a) What are three similarities and the cardinal difference between the main economic models of the Theory of the Consumer and the Theory of the Firm? 5

b) You can choose between spending your time studying economics or having fun! You figure out the maximum number of hours you can study (no fun!) or have fun (no studying!) per week. You also know your study/fun utility function (after all, you are becoming an economist). How can you find out your best combination of study and fun? 5