Suppose that a firm’s production technology is described by the production function f(x1, x2) = (x1)^2x2, where x1 denotes the quantity of input 1 and x2 denotes the quantity of input 2. Let the price of input 1 be $1 and the price of input 2 be $4. a. Derive the conditional input demand functions for both inputs. b. Derive the firm’s cost function
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Suppose that a firm’s production technology is described by the
production function f(x1, x2) = (x1)^2x2, where x1 denotes the quantity of
input 1 and x2 denotes the quantity of input 2. Let the price of input 1 be
$1 and the price of input 2 be $4.
a. Derive the conditional input demand functions for both
inputs.
b. Derive the firm’s cost function
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- The cost function for producing x items is C(x)=x2-3x+625. a.Find the average cost function. b.What is the minimum average cost? c.Find the marginal cost function. d.Is the point of intersection of the average cost and marginal cost function the same which produced the minimum the average cost? 2.Determine where the function f(x)=4x3-3x2+6 is concave and where it is convex. 3.An efficiency study conducted for Spektra Electronics Showed that the number of Base Commander handsets assembled by the average worker t hours after starting work at 8 a.m is given by N(t)=-t2+6t2+15t (0t4) At what time during the morning shift is the average worker performing at peak efficiency?Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?A street musician bought a new fiddle for $850.00. Assume she breaks 1 string each hour and can buy new strings for $1.00 each. On average, she makes $18.00 per hour. (a) Find the cost function C(x) associated with playing the fiddle for x hours. C(x)= (b) Find the revenue function R(x) for the amount of revenue gained from x hours of playing R(x) = (c) Find the profit function P(x) for the amount of profit gained from x hours of playing P(x) = (d) Use the functions above to complete the following sentence. She will need to work hours to break even