ECON 100A Practice Midterm II

Transcription

1 ECON 100A Practice Midterm II PART I 10 T/F Mark whether the following statements are true or false. No explanation needed. 1. In a competitive market, each firm faces a perfectly inelastic demand for its products. 2. If MC is greater than AC everywhere, then the firm has decreasing returns to scale. 3. If wages permanently increase the isocost becomes steeper. 4. A risk neutral person has a constant marginal utility. 5. A firm that has increasing returns to scale for small quantities and decreasing returns to scale for larger quantities will produce when returns to scale are increasing. 6. Both Ad-valerum and specific tax will change the market supply curve. 7. EV > CV for an inferior good.

2 8. Average fixed costs never increase as output increases 9. Biased technological change causes output to increase without changing the ratio of inputs of production. 10. MRTS for perfect substitutes is constant. PART II 3 SHORT ANSWER QUESTIONS 1. Graph three sets of short-run MC and ATC curves that are consistent with a firm having constant returns to scale in the long-run. Add the LR supply curve to your graph. The LRS is the envelope of SR AC. Therefore the SR AC all have their minimum at the same quantity.

3 2. State the conditions for perfect competition. Explain why firms in a perfectly competitive market have zero profits. Identical goods, full information, constant input prices, low transaction costs, free entry and exit. Since there is free entry to the market, if firms in this market are making a profit, more firms will enter the market all the way to the point where firms make no profits. 3. Consider a firm with Cobb-Douglas production function. Currently the firm is producing 100 cell phones at cost minimizing-point. a. Draw an isocost and an isoquant that are consistent with the scenario (point A). b. The firm wants to expand production to 200 units. Add to your graph the capital and labor choice of the firm in the short run (point B) and long run (point C) and mark the LR and SR expansion paths. c. Graph MC and ATC curves that reflect the 3 points of production you marked in parts a and b. (hint: where is the LR cost minimizing point? You should have 2 different sets of short-run ATC &MC)

4 A & C are the cost minimizing points when the SR ATC hits its minimum. B & C both produce Q = 100, but point B is on the original MC/ATC curves with the original level of capital. Point C is producing 200, but minimizing costs. Long-Answer Question #1 Let Q = K L 1/3 a. Does this production function has increasing, decreasing or constant returns to scale? Show your answer mathematically. IRTS Q(2K, 2L) = 2 4/3 K L 1/3 > 2Q = 2 K L 1/3

5 b. Now let K = 4, wage = 4 and r = 20. i. Find total costs in the short-run. L = (Q/4) 3 TC = 4*20 +4 (Q/4) 3 = Q 3 /64 = 80 + Q 3 /16 ii. Let market price be $9. Find the profit maximizing quantity and find profit at that quantity. Will the firm produce at this price? Why or why not? P = MC 9 = 3Q 2 /16 -> Q = sqrt(48) ~7 Profit = 9*7 ( /16) = = The firm produces since AVC<p AVC = Q 2 /16 = 48/16 =3 < 9 iii. Given the quantity you found in (ii), how many units of labor are hired? L = (Q/4) 3 = (7/4) 3 = 5.36 iv. Now find the expression for the cost-minimizing quantity of labor in the long-run. Given 4 units of capital and input prices as above, how much labor should the firm use? Explain why your answer is different than the amount you found in (iii). MPL/MPK = K/3L = 4/20 -> L = 5K/3 If K = 4 then L = 20/3. These are the cost minimizing levels of capital and labor. Given these quantities Q = 4*(20/3) 1/3 = 4*1.88 = 7.52, which is higher than the quantity produced in the short run. In the LR the firm can adjust capital and labor to minimize costs.

6 Long-Answer Question #2 The San Diego market for surf lessons is perfectly competitive. In the long run, firms have a U-shaped average cost curve. The market is characterized by free entry and exit. All firms are identical. The government decides to require surf instruction firms to be licensed and the price of a license is a flat fee of T for each firm. Assume that the market demand for surf lessons is downward sloping. a. Show what happens to the firms' average cost and marginal costs curves. Average cost shifts up, marginal cost does not change. LRS shifts up to where the new AC curve cuts through the MC curve. b. Show what happens to long run market supply and equilibrium market price and quantity. Equilibrium market quantity goes down, price goes up. c. Has the number of firms increased or decreased? Explain. The number of firms must decrease. Since quantity produced by the firm increased, but market quantity decreased it means that the number of firms decreased. d. Has the output of the average firm increased or decreased? Explain. The firm s output has increased (MC cuts through the new AC at a higher quantity) e. Show on the market graph the change in consumer surplus. Marked in yellow.

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