2. Assume the technology is described by y =(x,x2)i and that prices of inputs are wi and wzrespectively. (a) Find the conditional factor demands for inputs x, and x2
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- A purely competitive firm has a single variable input < (labor), with the wage rate. W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) what is the first-order condition for profit maximization ? Give this condition an economic interpretation. (c) What economic circumstances would ensure taht profit is maximized rather tahtn minimized?A firm uses capital and labour to produce widgets . In the short run capital is fixed ,while labour is variable . The short-run production is X = -L^3 +24l^2 +240L where X is the number of widgets produced in per week,and L is the number of workers employed .Each worker works a 40-hourweek. The wage rate is $12 per hour. a. Calculate the ranges of variables for L over which the firm is in stage 1,2 and 3 b. What is the minimum product price at which the firm will operate in the short run? c. The product price, over which the firm has no control is such that the firm's maximum posible pure profit $ 1096 per week. In order to achieve that level of profit it must employ 16 workers .How much is the firm's total cost?.Given the following cost function, determine the underlying production function. 1 2C(m, w, y) = 10mwy, where y is the output and m and w, are the prices of two inputs x1 and x2 respectively.
- Let f(x1, x2) = (min{x1 − x1})α1(min{x2 − x2})α2where x1, x2 > 0 are interpreted as minimum requirements of inputs needed for thefirm to operate, and α1, α2 > 0, with α1 + α2 = β < 1. Draw some isoquants, and obtain the cost function and the conditional demands for inputs. min {x-xbar} means {0, x-bar}Minimization CT = W1X1 + W2X2 Hold it: Y = X11/3 X21/6 where X1 and X2 are the productive factors and W1 and W2 are their prices, respectively. Determine: If X2 = 27 and W2 = 2 a) The short-run cost functionSuppose the wage rate is $10 and the rental rate on capital is $20. Consider the total cost line associated with a total cost of $200. The intercept of this line on the X-axis (capital axis) is _______ and its slope is_____. A. 20, -2 B. 10, -2 C. 10, -1/2 D. 20, -1/2 Clear my choice
- A firm has two variable factors and a productionfunction f(x1, x2) = 6x1/21X21/3. The price of its output is 3, the price of factor 1 is 3, and the priceof factor 2 is 2.– What is the optimal production output level?– What is the maximum profit-level?A manager hires a labor and rents capital equipment in a very competitive market. Currently the wage rate is Gh₵ 2 per hour and capital is rented at Gh₵ 5per hour, the unit price of the product is Gh₵ 0.25 and total cost is1000. Suppose the firm’s production is as follows: Q =14K⁰L⁰+10 Required What is the amount of labor and capital the firm should employ in order to maximize profit. What is the maximum profit.A purely competitive firm has a single variable input L (labor), with the wage rate W0 per period. Its fixed inputs cost the firm a total of F dollars per period. The price of the product is P0. (a) write the production function, revenue function, cost function, and profit function of the firm. (b) What is the first-order condition for profit maximization? Give this condition an economic interpretation. (c) What economic circumstances would ensure that profit is maximized rather thatn minimized?
- Consider the cost minimization problemMin C(x1, x2) = w1x1 + w2x2S.t x1ρ + x2ρ = yρDerive the conditional factor demand functions?Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of managers decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition?A football producer has available Rs.200. What will be the slope of iso-outlay line when, price of input A=Rs.3 and price of input B=Rs.1.5
