Numerade

Questions asked

INSTANT ANSWER

QUESTION ONE Given indirect utility function of the nature \( V(P, M)=\frac{M^{2}}{4 P_{1} P_{2}} \) i. Derive the ordinary demand functions ii. Derive the associated expenditure functions iii. Suppose \( M=100 P_{1}=5 \) and \( P_{2}=4 \), calculate the total effect, substitution effect and income effect as a result of changes in \( \mathrm{P} \) and \( \mathrm{M} \)

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ANSWERED

Shu Naito

Numerade educator

c) A firm's profit function for a certain product is given as pi(P) = P^3(frac{1}{w_1} + frac{1}{w_2}). The product sells at Tshs 10 per unit. The prices of inputs 1 and 2 are Tshs 50 and Tshs 100 respectively i. Find the level of the output that will maximize profit (4 Marks) ii. Determine the optimal levels of factor use which maximize profit (4 Marks)

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INSTANT ANSWER

Assume a utility function is \( U\left(X_{1}, X_{2}\right)=X_{1}^{a} X_{2}^{1-a} \quad 0<a<1 \) a) Derive the uncompesanted demand function and indirect utility function (7 marks) b) Verify the symmetry restriction of the slustky substitution matrix (5 marks) \[ 2 \text { of } 4 \] c) Derive the expenditure function and compensated demand function (7 marks) d) Based on the results on (c) above verify the Shephard's Lemma (6 marks)

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ANSWERED

Shu Naito

Numerade educator

b) Consider the following profit function that has been obtained from a technology that uses single input a \( \pi(P . W)=P^{2} W^{\beta} \) Where P is the output price and W is the input price and ß is a parameter value 1)For which values of ß the profit function is a real profit function with all of the appropriate properties? 2)Calculate the supply function of the product and the demand for inputs

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Kelvin c.