Basic Homework Questions

1. For each of the following production functions (s and b) (b) What is the firm's long-run average cost curve? find the following equations (i-iii) in terms of Qo, w and (c) Over what range of output does the production r. function exhibit economies of scale? i) MRTSL ,K (d) Over what range of output does the production ii) Long-run capital and labor demand curve. function exhibit diseconomies of scale? ii) Long-run total cost curve. 5. The following incomplete table shows a firm's various iv) Short-run capital and labor demand curve if the firm coats of producing up to 6 units of output. Fill in as is stuck with K = 4. much of the table as possible. If you cannot determining v) Short-run total cost if the firm is stuck with K = 4. the number in a box, explain why it is not possible to do (B) Q = 71 KM/ TO TVC AFC AC MC AVC TFC (b) Q = LK +5L 163 2. Cars must be produced with 4 wheels and 2 doors for each car. For example, if you have 5 wheels and 2 doors 2 then you can only produce one car (and you have one 3 213 10 extra wheels that gets wasted). Let ( be the number of cars, W be the number of wheels, and D be the number of doors. The price of one wheel is Pw and the price of 5 26 one door is PD. G 144 (s) Determine three (W, D) points on the Q-10 iso- quant (what combinations of inputs lead to produc- tion of 10 cars). (b) What is the long-run total cost function for pro- ducing cars, TC (Q, Pw, PD)? (Hint: think of this na intuitively rather than using formulas. For example, what is the cheapest way to produce one car? Two jmolina3 cars? ( cars?) (c) What is the production function for cars Q (W, D)? (This tells how many cars can be produced for each combination of W and D) 3. The processing of Q vaccination appointments can be lina3 imolin done using hours of computer time (denoted by K") and hours of human time (denoted ). The processing of 2 = 400 vaccination appointments requires either 4 hours of computer time ( = 0 and K = 4) or 20 hours of human time (L = 20 and K = 0). Hours of computer time and hours of human time are perfect substitutes; for imolina3 example, the processing of ( = 400 vaccination appoint- ji ments could also be done using K = 2 hours of computer time and L = 10 hours of human time. (a) Determine 4 points on the Q = 800 isoquant. (b) Write out the equation for the production function Q ( L, K). lina3 jmolin (c) Determine the labor and capital demand in terms of Qo, w and r. (d) Determine the total cost in terms of Qo, w and r. 4. A firm's long-run total cost curve is TC(Q) = 76Q - imolina3 56Q2 + 4Q3. (s) What is the firm's long-run marginal cost curve