Cobb-Douglas and utility function
Derive the consumer's optimal demand of x and y, respectively, when the budget constraint is px + qy = m and the utility function is x^p + y^p.
What I've done so far :
Deriving with respect to x and y:
px^p-1
py^p-1
Then:
(px^(p-1))/(py^(p-1)) = (x/y)^(p-1)
I'm lost after that. Please help me with steps
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Complete parts a-e. 1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint:...
Complete parts a-e.
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Complete parts a-e.
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2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in...
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2) A consumer's utility function is a(x,y) = (a) Find the consumer's optimal choice for x as a function of income I and prices px,Py' (b) Sketch the demand curve for x as a function of its own price Pz when py = 10, 1 = 100. (It may be easiest to plot a few points.)
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is I. His utility 18 * and y. Px is the price of x. Py is the price of Is 1. His utility is given by U(x,y) = xy a) Calculate consumer's optim uncompensated demand) s optimal choice of x and y under his budget. hinc b) Derive the indirect utility function. c) Are these two goods normal goods? Why! d) Derive the expenditure function....
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