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An individual purchases quantities a, b, and c of three different commodities whose prices are p, q, and r, respectively. The consumer spends m dollars, where m > 2p, and the utility function is given by
U(a,b,c)= a+ln(bc)
Show that the optimal expenditure on the second and third good is equal to p (that is, show that when utility is maximized, the expenditure on each of the second and the third good is equal to p).
Find a, b, and c when utility is maximized (you may assume Lagrange multipliers corresponds to the maximum solution).
State whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L.
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U(x,y)=3x+y, where x and y represent the quantities of two goods, X and Y. The ocnsumer has I=60 , to spend on the two goods, and good Y costs Py=2 per unit. The price of good x, Px is also exogenous. Calculate the consumer's elasticity of demand for..
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