Simplify each of the following expressions. (2 points)
(i) (x0.5 + x3/4x-1/4)/x0.25) (ii) x-2×3/2/x1/3 (iii) (x1/4y-2)-3 (iv) (64×9)1/3 (16y)-2
Consider the consumer demand function for blueberries: Q = P-aRb Xc where a, b and c are positive constants, Q = quantity of blueberries demanded, P =price of blueberries, R= price of raspberries, and X= consumer income.
Suppose the initial values of P, R and X are P0, R0 and X0. Now both P and R rise by 20 percent
(X remaining unchanged). Show how demand Q would change as a result? Specifically, would demand rise by more than 20 percent, less than 20 percent, or by 20 percent? Show your work. (3 points)
Economic theory tells us that if P, R and X all rise simultaneously by the same percentage, demand Q would not change? In the demand function given above, what condition would ensure this? Explain. (2 points)
Find the natural logs of each of the following economic relationships:
α βProduction function in time period t: : Qt = Kt Lt , where K and L are factors of production such that
Kt = K0eut, Lt = L0evt, Q is output, and α, β, u, v, L0, and K0 are all constants. (3 points)
Revenue function: R= PQ, where P=aQ-b is the demand curve for the product, and
Q = [hKu + (1-h)Lu] r/u, where a, b, r and u are constants. (3 points)
Present value: V = y/(1+i)n , where V is the present value of a sum of money y to be received n years ahead, and i is the rate of interest. (2points)
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