Erin receives utility from consuming food (F) and clothing (C) as given in the utility function U(F, C) = 20F ^ 4 * C ^ 4 In addition, the price of food is $2 per unit and that of clothing is $10 per unit and weekly income is $50.

Using the above information solve the following problem:

a) Write and draw Erin's budget constraint along with its slope.

b) Derive the MRS of cloth for food of Erin?

c) Find the utility maximizing bundle of Erin. Explain the equilibrium point with the help of a diagram