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Suppose a firm's production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by:
MPL = , and MPK = .
a) Suppose the price of labor is w = 24, and the price of capital is r = 6. Derive the firm's total cost function.
b) What is the firm's marginal cost?
c) For this problem, you will sketch the graph of the firm's isoquant for Q = 20 units of output, and on the same graph sketch the firm's isocost line associated with the total cost of producing Q = 20 units of output. To get this total cost, you must use the Total Cost function from part a). Please scale your graph up to 100 units of Labor on the horizontal axis, and 100 units of Capital on the vertical axis (do not go above 100 units on either axis). For the isocost line, clearly identify the vertical and horizontal intercepts. For the isoquant, clearly identify 5 combinations of Labor and Capital that will produce Q = 20 (including the bundle that minimizes the firm's cost of production). Make sure your graph is neatly and accurately drawn and carefully labeled.
Find (all) the partial derivatives (e.g. ?u/?x and ?u/?y) of the following functions: 1. Q(p,I) = 300 - 3p - 4I 2. u(x,y) = 10xy 3. u(x,y) = ax? y? 4. z = (x+y)2 5. z = 2x3-11x2y +3y2
The parents of a young child decide to make equal annual payments into a savingsaccount, with the first payment being made on the child's fifth birthday and the last payment being made on the fifteenth birthday. Then a rotal of four withdrawals of..
Lenny's, a national restaurant chain, conducted a study of factors affecting demand. The following variables were defined and examined for a random sample of thirty of its restaurants:
A multiplicative demand function form: Qd= a*P^b1*Y^b2*Po^b3 is determine using cross sectional data and 224 observations. The regression results were given below:
Provide three examples of operating firm formed as, sole proprietorship, partnership and corporation. Describe how you decided on categorizing them.
Calculate the value of each of the following, before the tax and after the tax, to complete the table that follows: 1. The Equilibrium quantity produced Equilibrium Quantity (Millions of units) Before tax? After tax? 2. The equilibrium price consume..
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (F) at which a certain reaction starts to take place. Suppose that the two random variables X and Y have a joint density function f(x,y)= y, 0
Calculate the t-statistic for the hypothesis test c.) Find the critical value and rejection region for a 5% significance level d.) Given your answers to b.) and c.), what do you say to the athlete's statement that he is better than Carl Lewis? 2. ..
A firm sells its product in a perfectly competitive market where other firms charge a price of $130 per unit. The firm's total costs are C(Q) = 40 + 10Q + 2Q2. a. How much output should the firm produce in the short run?units
In this question we are going to incorporates investment in human capital by agents, in a form similar to physical capital. Labor units are replaced by human capital units Y = AK?(?H)1?? where • H ? Units of Human Capital • ? ? [0, 1] ? Fraction of..
.What are the equlibrium quantities (q1, q2 %u2026 ,q10)?. A-q1, q2 %u2026 ,q10 = 2B-q1, q2, %u2026 ,q9= 2 q10=1/2c-q1, q2, %u2026 ,q9= 3/2 q10=1/2d-q1, q2, %u2026 ,q9, q10= 3/2e- q1, q2, %u2026 ,q9= 3/4 q10=1/2f-q1, q2, %u2026 ,q9= 3 q10=1/2g-non..
Suppose xt = (1:05)t and yt = (1:02)t. Calculate the growth rate of zt in each of the following cases: a) z = xy b) z = x=y c) z = y=x d) z = x^1/2 y^1/2
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