Questions 1. (Cost Minimization, 10pts) The production functions are given as below. (1) Fill in blank cells in the table below.

(2) Using the table above, when Q=30, w = 1, and r = 2, find optimal inputs for five production function. (3) Using the first two production functions, graphically describe cost-minimization problems with a figure.

Now we will start comparative statics analyses. Suppose the price of "equipment" becomes relatively cheaper (i.e., r is reduced from 2 to 1).

(4) Using the last two production functions, graphically show how a producer's input choices respond to a price decrease with figures.

(5) Provide an example of two production functions - the one with high substitution between labor and capital and the other one with low substitution between labor and capital.

Questions 2. (Profit Maximization and Determinants of Supply Curve, 26pts) Suppose

q = AK1/3L2/3 (1)

where K is capital and L is labor in a Cobb-Douglas production function. (1) Derive optimal K and Lwith respect to A,q,w, and r.

(2) Examine whether marginal product of capital is diminishing.

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(3) Get Return To Scale for this function. Does MRTS diminish as L increase?

(4) Derive total cost (TC) with respect to r,w,q, and A.

(5) Provide marginal cost (MC) and average cost (AC) with respect to r, w, q, and A.

Now suppose p = 4 is given in the perfectly competitive market.

(6) Specify the profit function with respect to p, q, r, w and A.

(7) Describe the profit-maximization problem.

(8) For the production function in (6), determine the sign for marginal effect with respect to p, q, r, w and A (e.g., pro f it , pro f it , p q

profit, profit,and profit). r w A

(9) Using the function in (6), show that how a reduced r affects the profit while holding everything else fixed.

(10) When there is an increase in A, how it affects the optimal inputs choice and the profit? In the long-run, how it affects industry

supply and the price level?

(11) Draw a figure for the supply curves that show a comparative analysis of a reduced r. Show how the supply curve changes using

a figure with q at the horizontal axis and marginal cost at the vertical axis.

(12) Draw a figure for the demand for K that show a comparative analysis of a reduced r. (13) Define technology or technological progress.

Questions 3. (Deriving Supply Curve, 20pts)

Ray owns a small business that operates in the perfectly competitive industry. The short-run total cost of production is STC(Q) =

40 + 40Q Q2 + 0.02Q3 , where Q is the number of quantity. The prevailing market price is $10 per unit. (1) What is the equation for average variable cost (AVC)?

(2) What is the minimum level of average variable cost?

(3) How many should Ray produce to maximize profit?

(4) What is Ray's maximum profit?

(5) Graph SMC, SAC, and the profit-maximizing quantity. On this graph, indicate the maximum profit (4 pts). (6) What is Ray's short-run supply curve, assuming that all of the $40 per day fixed costs are sunk?

The market demand curve is m D(P) = 50000 1000P, where D(P) is measured in thousands of units.

(7) Find the long-run equilibrium price, quantity per firm, and number of firms (6 pts).

Questions 4. (Tariff and Quota, 20pts)

Suppose domestic demand is given by Qd = 10 12 P and domestic supply is given by Qs = 2 + P.

World market could provide any quantities at price of 4.

(1) Draw a figure that indicates consumer surplus and producer surplus for a closed economy (i.e., no import).

(2) Draw a figure that indicates consumer surplus and producer surplus for a open economy (i.e., free trade).

(3) Draw a figure that indicates consumer surplus, producer surplus, gov't revenue for a open economy with a tariff of 2.

(4) Compare net benefits of (1) cosed economy, (2) open economy with free trade, and (3) open economy with tariff.

(5) Now suppose imposing quota of 6. Draw a figure that indicates consumer surplus, producer surplus, gov't revenue.

(6) Now suppose imposing quota of 3 and imposing tariff of 2 for beyond quota amount.

(7) Now suppose imposing quota of 2 and imposing tariff of 4 for beyond quota amount.

(8) Compare net benefits (5) and (6).

(9) For question (6), we can consider 3 units are imported by a country with FTA (i.e., no tariff) and for the rest of imports the tariff of 2 is imposed for the rest of countries. Compare net benefits for (3) and (6).

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(10) Compared to a free-trade open economy, who is going to benefit most and who is going to suffer most in the economy of (3)?

Questions 5. (Subsidy and Dumping, 10pts)

Suppose domestic demand is given by Qd = 30 21 P and domestic supply is given by Qs = 2 + P.

World market could provide any quantities at price of 6. Now, foreign govenment pay 2 as a subsidy for each export product (this is called as dumping).

(1) Suppose importing country is a free-trade open economy. Draw a figure that indicates consumer surplus and producer surplus when a foreign country engages in dumping.

(2) Suppose importing country is a free-trade open economy. Draw a figure that indicates consumer surplus and producer surplus when a foreign country does not engage in dumping.

(3) Compare Net benefits between (1) and (2).

(4) Now domestic government does also pay subsidy of 2 per unit sold to domestic firms and a foreign country engages in dumping. Draw a figure that indicates consumer surplus, producer surplus, gov't expenditure, and net benefits.

(5) Compare (1) and (4). Who is going to benefit most and who is going to suffer most in the economy of (4).

Questions 6. (The Sources of Economic growth, 20pts)

Suppose the following production function, y = AK (qL)1 .

(1) What are the sources of economic growth (i.e., growth of y)?

(2) What are the sources of economic growth at the steady-state?

(3) What are the sources of economic growth at the transitional path?

(4) Describe the motion for K and q.

(5) In your analyses in (1), (2), and (3), what are exogeneous variables and what are endogeneous variables?

(6) Consider the solow model in HW5. Suppose saving rate decreases as people value more of present than future. What is the consequence to economic growth?

(7) Suppose people invest more on their education. Evaluate the consequence of increasing valuation of education on economic growth.

For the rest of the questions, refer to the following article, https://voxeu.org/article/new-ideas-about-new-ideas-paul-romer-nobel- laureate

(8) What are the main source of increasing return to scale technology? Please provide an example of production other than provided in the article.

(9) What is the implication that the production technology is increasing return to scale for an economic growth model? (10) Suppose government introduce digital service tax. How does it affect on economic growth model?