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A person has utility function U=4x^o.5Z^0.5 for goods X and Z at prices PX = $8 and PZ = $32 and income Y = $3200. The marginal utilities of the X and Z are: MUX = 2X^–0.5Z^0.5 and MUZ = 2X^0.5Z^–0.5 A)Graph the budget constraint (place Z on the horizontal axis, X on vertical axis.) Document the intercepts and slope of the constraint. B) Find the utility maximizing consumptions of X and Y given these prices and income. Explain your work and show on your graph. C) PZ decreases to $16. Show graphically and find the new utility-maximizing amount of Z. D) Sketch out the person’s demand curve for Z. E) Explain precisely how/why the price paid for an additional unit of Z can represent its marginal value to this consumer.