HELP WITH THESE QUESTIONS. Futons Inc. produces futons using only two inputs cap

Question

HELP WITH THESE QUESTIONS.

Futons Inc. produces futons using only two inputs capital (wood, nails, and hammers) and labor (measured in worker hours) - with a technology characterized by the following function: q = 2ln(K + 3L) Futons Inc. spent SI 00 on 100 units of capital at the beginning of the period. They can neither purchase nor sell units of wood, nails, and hammers until the end of the period, but the material docs not lose any value over time. Solve for the average product of labor and the marginal product of labor. Assuming that futon makers earn a wage of $9 per hour and the prevailing interest rate in the economy is 10 percent, solve for short run costs as a function of the numbers of futons produced. Consider a firm with the production function, q = (K^1/2 - L^1/2)^2. In the short-run, the level of capital is fixed. Determine the equations for MP_L and AP_L. Solve for the short-run cost function (i.e. total costs as a function of output) Determine the equations for MC, ATC, AVC, and AFC.

Explanation / Answer

a) Average product of labor is Q/L hence, APL = 2In (100 + 3L)/L since K = 100 is fixed.

Marginal product of labor derivative of total product wrt to labor so MPL is Q'L = 6/(100 + 3L)

b) In the short run, Futons spends a cost of $100 on capital, a rental price of 10% on the capital as implicit cost and a $9 per hour variable cost for L number of labor hires.

Let the cost fucntion be TC = rK + wL

Susbstitute K = 100, r = 10%, and w = 9

= 100*0.1 + 9L

Hence the short run cost function is TC = 10 + 9L.

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