1.) Consumer's utility function is represented by U = 40X**Y\"%, In this utility function, U is the total utility while X and Y are two outputs in the consumer's basket. The corresponding marginal utilities function will be MU, = AU/AX = 10X7Y\" and MU, = AUJAY = 30X***Y* for output X and Y respectively. Using these marginal utility functions, the relevant marginal rate of substitution MRS = - MU,/ MU, = - 20X 75Y75[30X**Y** = -1/3Y/X. Using the information provided in this item, answer the following questions. i.)What is the meaning of the marginal rate of substitution (MRS) of -1/3Y/X? Why is the MRS preceded by a negative sign? What is the relevance of this MRS to the consumer? ii.)The prices of both outputs is 5 pesos (that is P, = 5 pesos = P,) and consumer's income is equal to 50,000 pesos. What is the consumer's optimal condition considering marginal utilities, output prices and consumer's income? iii.)What will be the optimal combination of outputs X and Y considering output prices and consumer's income? iv.) The government imposed a 10% excise tax on the price of output X such that price of output X becomes P, tax = 5.5 pesos. What will be the optimal combination of output X and Y considering the higher price of output X, the old price of output Y and the same consumer income? 2.)In a monopoly, the market demand function is P = 40,000 -5Q ( while the marginal revenue function will be MR = 40,000 -10Q). The total cost function of the monopolist is TC =10x10 + 0.4Q + 0.002Q\" in which case the relevant marginal cost function of the monopolist will be MC = 0.4 + 0.004Q. In this instance, the average total cost function can be indicated as ATC = TC/Q = 10X10%/Q + 0.4 + 0.002Q. Use the information provided in this problem to answer the following questions. i.)What is the profit maximizing output level for this monopolist? What is the profit maximizing price for this monopolist? ii.)What is the total revenue, total cost and total profits at the profit maximizing output level? iii.)What is(are) the break even quantity(ies) for this monopolist? [Use the quadratic formula __ bxVbZ-4ac ] 2a 1.) Consumer's utility function is represented by U = 40X**Y\1.) Consumer's utility function is represented by U = 40X**Y7%, In this utility function, U is the total utility while X and Y are two outputs in the consumer's basket. The corresponding marginal utilities function will be MU, = AU/AX = 10X7Y\" and MU, = AU/AY = 30X*Y* for output X and Y respectively. Using these marginal utility functions, the relevant marginal rate of substitution MRS = - MU,/ MU, = - 20X 75Y?75[30X***Y"*** = -1/3Y/X. Using the information provided in this item, answer the following questions. i.)What is the meaning of the marginal rate of substitution (MRS) of -1/3Y/X? Why is the MRS preceded by a negative sign? What is the relevance of this MRS to the consumer? ii.)The prices of both outputs is 5 pesos (that is P, = 5 pesos = P,) and consumer's income is equal to 50,000 pesos. What is the consumer's optimal condition considering marginal utilities, output prices and consumer's income? iii.)What will be the optimal combination of outputs X and Y considering output prices and consumer's income? iv.) The government imposed a price floor on the price of output X such that price of output X becomes Py floor = 6 pesos. What will be the optimal combination of output X and Y considering the higher price of output X, the old price of output Y and the same consumer income? 2.)In a monopolistic competitive market, the total cost function of a firm is TC = 45x10 + 0.5Q + 0.003Q\"* (in which the Qarc min = 122,474.49 units, ATC.,, = 735.35 pesos) The average total cost and marginal cost functions of the firm can be given as ATC = 45x10%/Q + 0.5 + 0.003Q and MC = 0.5 + 0.006Q. i.)The demand for this firm is P = 100,000 -5Q (MR = 100,000 -10Q). What is the Q,, ., given the market demand? Whatisthe average total cost at maximum profits? What is the profit margin at the Q .., level? ii.)When a new firm (with a slightly differentiated output but remains a close substitute to the output of this firm) enters the market, the demand for the firm shifts to P' = 60,000 -5Q(MR' = 60,000 -10Q). What is the Q,, ,x given the reduced market demand? What is the average total cost at the changed profit maximizing output level? What is the profit margin at the Q' . level? iii.)Do you agree that the firm's profitability is likewise reduced by the entry of a new firm? Answer yes or no but justify your answer using information generated in this problem. iv.)Do you agree that the firm's productive efficiency is reduced by the entry of a new firm? Answer yes or no but justify your answer using information generated in this