Solution:
18. At the kink, x1 = 2*x2, the point given is x1 = x2 = 4
The given point gives utility = min{4, 2*4} = min{4, 8} = 4
Notice, that with x1 = 4, increasing x2 any beyond 2 (as at kink 4 = 2*x2 , so x2 = 2) will not increase the utility. So, marginal utility from good 2 is 0 (if you increase x2 by 1 more unit, so x2 = 5, utility is still 4). Notice, however increasing good 1 by 1 unit, will generate utility = 5, so marginal change in utility due to an additional consumption of good 1 is 1. Thus, correct option is (B) 1; 0
19. With production function of Y = 2L + 10K, L and K act as perfect substitutes in production of Y. Note that marginal product of labor, MPL = 2 and marginal product of capital, MPK = 10, so marginal rate of technical substitution = MPL/MPK = 2/10 = 0.2
Now, wage to rental rate ratio = w/r = 2/8 = 0.25
Clearly, wage to rental rate ratio = 0.25 > 0.20 = MRTS, implying that relative marginal cost of hiring labor is more than relative marginal benefit of labor (or in other words, relative marginal cost of hiring capital is lower than relative marginal benefit of hiring capital). So it would be beneficial to hire only the capital (since capital and labor are perfect substitutes in production).
Thus, for Y = 50, using the production function, we have 50 = 10*K, K = 5
Total cost = w*L + r*K
TC = 2*0 + 8*5 = $40
So, correct option is (A) $40.
18. Supposex, and x2 are used in fixed proportions such that y = mink,,2x2). At the point x1 = x2...
A consumer has utility function: u(x1 , x2 ) = x1 + 2x2 . The consumer has income m > 0 tospendongood1andgood2. Ifthepriceofx1 isp1 =1andthepriceofx2 isp2 =0.5, then, in order to maximize her utility, the consumer must consume: a) x1 = x2 (b) x1 = 2x2 (c) 2x1 = x2 (d) x1 = 4x2 (e) None of the above
2. Consider the following production function with two inputs X1 and X2. y = x1/2x2/4 a. Derive the equation for an isoquant (assuming X2 is on the y-axis). b. Derive the marginal product of input x1. c. Derive the marginal product of input x2. d. Derive the marginal rate pf technical substitution (MRTS).
uestion 3 (1 point) the production function is f(x1, x2) = x1/21x1/22. If the price of factor 1 is $10 and the price of factor 2 is $20, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Question 3 options: We can’t tell without knowing the price of output. x1 = 2x2. x1 = 0.50x2. x1 = x2. x1 = 20x2. Question 4 (1 point) A firm has the production function f(X,...
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