\"n economy has two consumers, Consumer A and Consumer B. These two consumers get utility from consuming two goods, x and y. Consumer A has a utility function described by . Consumer B has a utility function described by . Consumer A is initially endowed with 50 units of x and 40 units of y. Consumer B is initially endowed with 50 units of x and 10 units of y. You can assume that the price of y () is equal to 1 for this question. a) With Consumer A in the bottom left corner and Consumer B in the top right corner, draw an Edgeworth box that shows the initial endowment in this economy. Be sure to clearly label the total number of units of x and y on each axis. b) Derive the contract curve for this economy and draw it on the Edgeworth box that you drew in part (a). c) Sketch indifference curves in the Edgeworth box that would make sense given the location of the endowment and the contract curve. Make it clear which indifference curve belongs to which consumer. The sketches don't have to be mathematically perfect, but show that you understand the general relationships. d) Derive the equation for Consumer A's demand for x in terms of and their income. You may also simply write Consumer A's demand function using the Cobb-Douglas "shortcut", but you must write a sentence or two explaining what it means intuitively regarding the consumer's spending pattern. e) Calculate the market price of x (). f) You do not have to show the math, but write a statement that describes how you would calculate the optimal bundles for each consumer. A couple of sentences is sufficient