A)T production isoquant can be plotted by simply plotting the coordinates on the x1-x2 plane.
B) Given is a linear production function, it has perfect substitutability between the factors , therefore logically that factor is used which is cheaper for the production process as compared to the productivity of that factor. This can be proved :
MRTS = MPx1/ MPx2 = 2/4 = =0.5
Given, Price Ratio = Px1/Px2 = 2/3 = 0.67
This implies x1 s half as productive as x2 but costs more than half that of x2, therefore, using x2 is a better deal.
From the isoquant and cost line, it can be seen that given the cost line , the highest isoquant that can be achieved is as shown (2x1 + 4x2 = 16) and it can be produced only using x2.
Hence , amount of factor1 is 0,
Amount of factor 2 is :
Hence, MC= MR gives , 6Q/4 = 4 which gives Q=8/3
Hence amount of factor 2 is (8/3)×(8/3) /4=16/9
2. A firm has two variable factors and a production function f(11, 12) = 211 +...
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,...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
a profit maximizing firm has a technology with the production function f(x1,x2) =x1^0.5 x2^0.5 can only use 4 units of x2 in the short run. what is the optimal amount of x1 to use in the short run if the price of x1 is $1 and price of output is $13 .how much output does the firm make ? sketch 2 isoquants on same axis for production function f(x,y) = min (y,x^2)
Consider a firm which produces a good, y, using two factors of production, xi and x2. The firm's production function is 1/2 1/4 = xi X2. (4) Note that (4) is a special case of the production function in Question 1, in which 1/4 1/2 and B a = Consequently, any properties that the production function in Q1 has been shown to possess, must also be possessed by the production function defined in (4). The firm faces exogenously given factor...
Please show all steps. The correct answer is E 20. A firm has two variable factors and a production function, f(x,x)= x,13 x,173. The price of output is 1, the price of factor 1 is wų, and the price of factor 2 is wą. What is the profit-maximizing level of input x;? A) 1/(9w/?w,?) B) 1/(9w,w,?) C) 1/(27w;w,?) D) 1/(15w, wn) E) 1/(27w, wn)
Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10. (5 points) (w1, w2) respec- (2) Suppose that the price of product is p, and that the prices of factors are tively. Find the factor demand function ri(w, w2, p), x1(w1, w2, P), the supply function y(w1, W2, P), and the profit function T(w1, w2, p). (10 points) Suppose that a firm has the production function (1) Draw an isoquant for f(x1,x2) = 10....
A firm uses two inputs x1 and x2 to produce output y. The production function is given by f(x1, x2) = p min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10. 4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
competitive firm produces output using three fixed factors and one variable factor. The firm’s short-run production function is q = 305x − 2x2, where x is the amount of the variable factor used. The price of the output is £2 per unit and the price of the variable factor is £10 per unit. In the short run, how many units of x should the firm use ?
1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order...