Production and Costs 6) (Hint: on this question you will likely want to use a calculator!) Alice owns and runs a factory that creates widgets using capital and labor. The table below summarizes the production and cost functions of Alice’s factory, where q, K and L respectively represent the quantity of widgets, capital and labor, and costs are given in dollars. Before starting this question it would be a good idea to compile all the relevant formulae on a single piece of paper! K L q FC VC TC AFC AVC ATC MC MPL 2 0 0 $18 $2/unit 0.25 units of 2 1 of output output/unit of labor 2 6 2 2 9 3 2 4 2.5 2 22 5 29 2 44 5 2 63 9 0.091 2 75 10 0.083 a. Given the above information, what is the cost of one unit of capital to Alice? b. How much labor is required to produce the first unit of output? What is the cost of a unit of labor? (Hint: you can figure this out using marginal cost and the marginal product of labor.) c. Fill in the blank cells in the table. Check to make sure that your numbers are consistent with each other! d. Does Alice’s factory exhibit diminishing marginal productivity of labor? How do you know? e. Is Alice’s factory operating in the short run or the long run? How do you know? f. If the price of a widget was $2.50, what quantity of widgets would Alice’s factory produce (assuming that Alice’s decisions do not affect the market price)? How large would her profit or loss be? g. What price is the shutdown price for Alice’s factory? (Hint: it is not $2!) h. If the above costs were also true in the long run, what price would widgets have to be sold for in order for Alice to break even? i. What quantity minimizes Alice’s average total costs? Perfect Competition
Production and Costs 6) (Hint: on this question you will likely want to use a calculator!) Alice owns and runs a factory that creates widgets using capital and labor. The table below summarizes the production and cost functions of Alice’s factory, where q, K and L respectively represent the quantity of widgets, capital and labor, and costs are given in dollars. Before starting this question it would be a good idea to compile all the relevant formulae on a single piece of paper! K L q FC VC TC AFC AVC ATC MC MPL 2 0 0 $18 2 1 $2/unit of output 0.25 units of output/unit of labor 2 6 2 2 9 3 2 4 2.5 2 22 5 29 2 44 5 2 63 9 0.091 2 75 10 0.083 a. Given the above information, what is the cost of one unit of capital to Alice? b. How much labor is required to produce the first unit of output? What is the cost of a unit of labor? (Hint: you can figure this out using marginal cost and the marginal product of labor.) c. Fill in the blank cells in the table. Check to make sure that your numbers are consistent with each other! d. Does Alice’s factory exhibit diminishing marginal productivity of labor? How do you know? e. Is Alice’s factory operating in the short run or the long run? How do you know? f. If the price of a widget was $2.50, what quantity of widgets would Alice’s factory produce (assuming that Alice’s decisions do not affect the market price)? How large would her profit or loss be? g. What price is the shutdown price for Alice’s factory? (Hint: it is not $2!) h. If the above costs were also true in the long run, what price would widgets have to be sold for in order for Alice to break even? i. What quantity minimizes Alice’s average total costs? Perfect Competition
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