Problem 1 Henrietta can buy rolled oats (X) for $3 per pack and yogurt (Y) for $1 per jar. The expression for Henrietta's expenditure varies with qx and qy according to the function E(qy, qY) = 3qx + qy. 1. Write the total differential of Henrietta's expenditure. (Keep in mind that given a generic function F(x,y), the function's total differential is dF = Fx dx + Fy dy where Fx and Fy are the partial derivatives of the function F with respect to x and y respectively) Along a budget constraint, Henrietta's expenditure remains constant and the expenditure's total differential dE is equal to zero. 2. Solve the dE = 0 equation for dqy/dqx. What is the slope of Henrietta's budget constraints? Does it vary with the quantity of rolled oats and yogurt she purchases? Henrietta's utility from rolled-oats and yogurt is summarized by the utility function U(qx, qy) = qx (qy - 4)2. 3. Write the total differential of Henrietta's utility function. Along an indifference curve, Henrietta's utility remains constant and her utility functions' total differential dU is equal to zero. 4. Solve the dU = 0 equation for day/dqx you find the slope of Henrietta's indifference curves. Does it vary with the quantity of rolled oats and yogurt Henrietta purchases