Derive the equation representing carinas demand for food

Question

Problem

Carina buys two goods, food F and clothing C, with the utility function U = FC + F. Her marginal utility of food is MU_F = C + 1 and her marginal utility of

clothing is MU_C = F. She has an income of 20. The price of clothing is 4.

a) Derive the equation representing Carina's demand for food, and draw this demand curve for prices of food ranging between 1 and 6.

b) Calculate the income and substitution effects on Carina's consumption of food when the price of food rises from 1 to 4, and draw a graph illustrating these effects. Your graph need not be exactly to scale, but it should be consistent with the data.

c) Determine the numerical size of the compensating variation (in monetary terms) associated with the increase in the price of food from 1 to 4.

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.