In this economy there are Gabby (G) and Millie (M) with goods X and Z. Gabby and Millie both have the same utility function U = 10X^0.8Z^0.2 with marginal utilities: MUX = 8X^-0.2Z^0.2 and MUZ = 2X^0.8Z^-0.8 Prices are Px = 8 and Pz = 1. Gabby has $500 income and Millie $200 income for X and Z.

a. Find the individual and total (market) quantities demanded for X and for Z at these prices. Suppose there are 140 Z's and 70 X's being supplied in this simple economy. Are the markets in a competitive equilibrium? Explain and illustrate the situation in a graph that shows the Production Possibility Frontier and the Edgeworth Box (with correct dimensions) - Graph good X on the horizontal axis of your graph(s) and Z on the vertical axis.

b. Show and explain why/how at the competitive equilibrium resources are allocated efficiently in this economy (i.e., efficiency conditions are satisfied.)

c. Now suppose that good X experiences a big increase in demand. Describe how the market, from an equilibrium situation, adjusts to the increase in demand. In your explanation just describe/illustrate the movements along, or changes to, your graphs/illustration above. A brief and general description is sufficient.