Reference no: EM132131757
Question -
a. A firm producing two products X and Y where x and y are the quantity of product X and Y produced respectively. If the firm produces on the same isocost and has a fixed cost of $1000.
Given the marginal costs, ∂C/∂x = 14xy + 15x2 and ∂C/∂y = 7x2 + 12y.
i. Show that (∂C/∂x)dx + (∂C/∂y)dy = 0 is an exact differential equation.
ii. Hence, solve the differential equation to find the total cost TC(x, y).
b. A firm produces two goods, X and Y. If x is the quantity of good X demanded and y is the quantity of good Y demanded and their corresponding prices px and py.
Given that the demand functions of the firm are: x = 2py - 4px + 80 and y = -2py + 2px + 50. Further, that the joint total cost function of the firm is C(x, y) = x2 + xy + 3y2.
i. Find an expression in terms of x and y for the profit function.
ii. Determine the quantities of x and y that maximizes the profit.
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