Consider a firm in a competitive market with market price p. Which of the following statements are true, which are false? In its optimization problem, a profit-maximizing firm takes into account the effect of the quantity O True O False it produces on the market price. In the long run it is optimal for the firm to produce the quantity q for which the difference between True False the marginal costs of producing q and the average costs of producing q is maximized. In the short run the firm makes a positive profit by producing a True False quantity q if the average variable costs of producing q are smaller than p.
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)(1) When chef Paolo prices his speciality ‘pizza-n-all’ meal at £25, he sells 20 meals a day. When he prices his pizza meal at £22, he sells 21 meals a day. Suppose Paolo reduces his price from £25 to £22. Explain the impact of the price reduction on the revenue he receives from the first 20 meals he sells. Total Revenue – Price X Quantity. Revenue @ £25 = £25 X 20 = £500. Revenue @ £22 = £25 X 20 = £440 The impact of the price reduction is a reduction in total revenue of £60 (-12%) over the first 20 meals that he sells. Calculate the additional revenue generated from the additional meals he sells when he lowers his price to £22. Total Revenue = Price X Quantity. Total Revenue @ £22 = £22 X 21 = £462. Additional Revenue = Revenue @ £25 – revenue @ £22 = £500 - £462 = -£38. Calculate the marginal revenue Paolo receives from the 21st meal. How does that amount relate to the amounts you calculated in (a) and (b)? (3%) Suppose Paolo reduces his price from £25 to £22. Explain…
- 1. (i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Drawthe budget constraint for a consumer with standard preferences. What is the slope of this budget constraint? (ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimalconsumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginalrate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For aconsumer with a constant income of £3,000, show what happens to consumption of juice and cheese.Decompose the change into income and substitution effects.An investor has a certain amount of money available to invest now. Three alternative investmentsare available. The estimated profit in Kwacha of each investment under each economic conditionare indicated in the following payoff table:Event Investment SelectionA B CEconomy declines 500 -2000 -7000No charge 1000 2000 -1000Economy Expand 2000 5000 20,000Based on his own past experience, the investor assigns the following probabilities to eacheconomic condition:( )( )( )Economy declines 0.30No change 0.50Economy expands 0.20PPP===i. Determine the optimal action based on the maximax criterion ii. Determine the optimal action based on the maximin criterion iii. Compute the expected monetary value (EMV) for each investment iv. Compute the expected opportunity loss (EOL) for each investment v. Explain the meaning of the expected value of perfect information (EVPI) in thisproblem vi. Based on the results of (iii) and (iv), which investment would you choose?vii. Compute the coefficient of…A firm's short-run production function is given with Q(K, L) = L0.2* K2 . Capital is fixed with K=3. The price of capital is r = 0.1 and the price of labour is w = 4 The price of the final output is p = 8 a) Do you think it is possible to depict this production function with an isoquant? Justify your answer by explaining the concept of an isoquant. b) Calculate the optimum quantity of labour the firm should use if it wants to maximize its profit. Also calculate the output produced and the corresponding profit.
- A market analyst working for a small appliance manufacturer finds that if the firm produces and sells x blenders annually, a model for the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.001x3 − 372. Graph the function P in an appropriate viewing rectangle, and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −263, so the firm loses $263.00 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the nearest whole number.) blenders(b) Does profit increase indefinitely as more blenders are produced and sold? YesNo If not, what is the largest possible profit the firm could have? (If profit increases indefinitely, enter your answer as ∞. Otherwise, round your answer to the nearest cent.)In the Walton Bookstore example with a discretedemand distribution, explain why an order quantityother than one of the possible demands cannot maximizethe expected profit. (Hint: Consider an orderof 190 calendars, for example. If this maximizesexpected profit, then it must yield a higher expectedprofit than an order of 150 or 100. But then an orderof 200 calendars must also yield a larger expectedprofit than 190 calendars. Why?)Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?
- A firm decides to invest x units of capital in project A and y units in project B. The expected return for 1 unit of investment is $400 in project A and $800 in project B. However, in order to meet the expectations of the firm’s ethical and environmental policy, the values of x and y must satisfy the constraintx2 + y2 − 4x − 6y = 67How many units of each type should the firm buy in order to maximize total return?In the time interval between t and t 1 seconds beforethe departure of Braneast Airlines Flight 313, there is aprobability pt that the airline will receive a reservation for 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1035 the flight and a probability 1 pt that the airline will receiveno reservation. The flight can seat up to 100 passengers. Atdeparture time, if r reservations have been accepted by theairline, there is a probability q(y|r) that y passengers willshow up for the flight. Each passenger who boards the flightadds $500 to Braneast’s revenues, but each passenger whoshows up for the flight and cannot be seated receives $200in compensation. Formulate a dynamic programmingrecursion to enable the airline to maximize its expectedrevenue from Flight 313. Assume that no reservations arereceived more than 100,000 seconds before flight time.J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. Atthe beginning of January, Huggys has a 30% market7.9 Conclusion 401share. During any month, 10% of the people whopurchase Huggys defect to brand X, and a fraction0.2a1y2 of customers who usually buy brand X switchto Huggys, where a is the amount spent on advertisingin millions of dollars. For example, if you spend $4million during a month, 40% of brand X’s customersswitch to Huggys. Your goal is to maximize J&J’saverage market share during the next 12 months,where the average is computed from each month’sending share. Determine an appropriate advertisingpolicy. (Hint: Make sure you enter a nonzero trialvalue for each month’s advertising expense or Solvermight give you an error message.)