1. [4 points] Suppose a representative consumer's preferences are represented by the utility function 1 3 U = x5 3.5. He has an budget of $96 allocated to the consumption of goods I and 'I". a. Determine his optimal consumption bundle if P3 = Slond Py = $2. {2] b. Suppose F3 decreases ta 51 while Py remains at $2. Determine his new optimal bundle. [1} c. Use your answers in a. and b. to calculate his relative demand for good X for (Px, Py) = ($2,$2) and (Px, Py) = ($1,$2). Use your calculated values to plot the relative demand curve for X. (1) PX (Dx, Dy) DX (Px, PY) PY RD for X = 1.2 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1 1.22. [5 points] Suppose the production functions of goods X and Y are given by Qx = Ly, Qy = 2 Ly. a. Calculate the output quantity at different values of Ly and use them to calculate MPLy. Is MPLy increasing, constant, or diminishing? (2) AQx Lx Qx = 1 MPLY = ALY 1 2 b. Calculate MPLy. Put your answer in the table. AQY Ly Qv = 2 Ly MPLY = ALY 1 4 Use your answer of MPLy with your answer of MPLy in part a to explain whether MRT is decreasing, constant, or increasing as more good X is produced. (1)c. Suppose MRS = 1