Let us suppose the market size is 22,218,564 for a self cooking oven. The imitation rate is 0.29 and the innovation rate is 0.006. Recall the Bass Model S-Curve function: n(t) = pm + (q-p)N(t - 1) — qN²(t − 1) m How many new users would there be at time period 2? Let us suppose the market size is 15,343,291 for a self cleaning oven. The innovation parameter is 0.009 and imitation parameter is 0.29. Recall the Bass Model S-Curve function: n(t) = pm + (q-p)N(t-1)- qN²(t-1) m How many total users would there be at the end of time period 2?
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- For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−90)^2+4,050. The maximum capacity of the company is 130 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! 1. Assuming that the company sells all that it produces, what is the profit function? P(x)= 2. What is the domain of P(x)? 3. The company can choose to produce either 50 or 60 items. What is their profit for each case, and which level of production should they choose? 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?Consider a Hotelling model with linear transportation costs. The consumers are located uniformly along a segment of unit length. There are two Örms, A and B, located at the opposite ends of the segment. Each Örm has zero marginal costs. The prices of the two Örms are equal to 1. The quality of each Örm is denoted qi, i = A;B, and each qi is uniformly and independently distributed over [2; 3]. Each Örm knows the values of both qualities while consumers know only the distribution (unless Örms disclose the quality). The gross valuation of the consumers for each Örm is the expected quality of that Örm given the available information. Their net utility is their gross valuation minus the transportation cost minus the price. Unit transportation costs are equal to 1. a. Suppose that Örms can simultaneously disclose their own quality qi at zero cost. Consumers then decide which product to buy. What is the equilibrium? Carefully explain your derivation and provide economic reasoning where…Which of the following is generally true of the experiments created by Kahneman and Tversky? Choose best answer: a. Individuals are generally indifferent between payouts in expected value and payouts in certainty in most situations. b. Individuals will generally take an expected value payment over a guaranteed payout in most gambling situations. c. Individuals will generally take a guaranteed payout less than expected value in most gambling situations.
- Consider the incomplete-information version of the spatial Bertrand model with firms i = 1, 2. For each firm, 25% of 1000 potential consumers are partially informed and only know about firm i’s product. The remaining 50% know about both firms’ products. Consumers are evenly distributed along a one-mile street and the shops are located at either end of the street. Assume all consumers have maximum willingness to pay of 16, (there-and-back) transport costs are 2, and the location of the indifferent consumer is xm = (p2 – p1 + t)/2, where pi is the price at shop i and t is transport costs. How much profit does each firm make if p1 = p2 = 12 and marginal (and average) cost c = 10 for both firms?Consider a population of consumers. When a consumer is a member of a club providing a level of provision G and having n members, they obtain utility Where k is a positive constant and G n is the charge for club membership. a. Derive the optimal membership for the club if it maximizes the utility of each member. b. Assuming the club chooses G optimally given its member ship; calculate the loss due to membership of a club with suboptimal size. c. Assume that the total population is of size m, with k d. What club size maximizes total utility produced by the club? Contrast to the answer for part a.A new market appears that works according to the rules of the Stackelberg model. The costs of firms on this market as a function of individual supply q is C(q) = f + Cq^2, where both F > 0, C > 0. The demand is P(Q) = A - BQ as afunction of total supply Q, with A > 0, B > 0. What is the quantity of followers on the market assuming free entry (as a function of A B C and F) Assume entry costs Z, what is the new equilibrium quantity of firms?
- Consider the online learning problem with demand learning. The firm sells a product without any historical demand information. In each period, the firm can set a price and would observe a demand based on the charged price. Suppose the true demand function in each period is D(p) = 9−3p+ϵ, where ϵ is a random variable with zero mean. The marginal cost is negligible. (a) What price should the firm charge if you know the demand function? What would be the expected revenue if the firm implements this price for n periods? (b) Suppose you do not know the demand function, but know that the demand is a linear function, and the slope is 3. In other words, you know that demand is D(p) = a − 3p + ϵ and would like to estimate a from the data. Suppose from the historical data, you have k pairs of demand and price, i.e., (p1, D1),(p2, D2), ...,(pK, DK). Suppose you would like to minimize the residual sum of square, i.e., min a X K i=1 (Di − a + 3pi) 2 . (1) What would be your best estimate of a?…Consider a rent-seeking game with N ≥ 2 contestants. The effort for person i is denoted by xi for i = 1; ... ; N. The cost per unit of effort is C. All contestants are identical. They value the rent at V and each contestant can win the prize with a probability equal to their effort relative to the total effort of all contestants. Thus the payoff function of person i exerting effort xi is given by Exercise 11.10 Three firms have applied for the franchise to operate the cable TV system during the coming year. The annual cost of operating the system is $250 and the demand curve for its services is P = 500 - Q, where P is the price per subscriber per year and Q is the expected number of subscribers. The franchise is assigned for only one year, and it allows the firm with the franchise to charge whatever price it chooses. The government will choose the applicant that spends the most money lobbying the government members. If the applicants cannot collude, how much will each spend on…For an output level exactly at QEQE, the value of a unit to a buyer is equal to the cost of a unit to a seller. Suppose a firm that produces for this market employs a private security force that makes town residents, many of whom have no business with the company, feel safer. This scenario is characterized by , which is an example of
- Actuaries perform the crucial task of estimating the time paths and probability distributions of costs and revenues for different insurance contracts. Becoming an actuary takes several years, and involves passing a series of rigorous examinations given either by the Society of Actuaries or by the Casualty Actuarial Society. Usually, the individual works for an insurance company while studying for the exams, and the company gives the individual time off to study for the exams. Passing an exam usually results in a significant pay increase. a) Do actuaries have general or firm-specific human capital? b) Who “pays for” the worker’s time off to study for the exams? Choose one answer and explain. · the worker does, by accepting a lower salary · the firm does, to invest in the worker’s human capital c) Why does the individual get a pay increase after passing each exam? Why not evaluate the employee once per year, like many companies do?One of the key provisions of the Affordable Care Act was the ensuring coverage for “pre- existing conditions,” which had formerly been excluded from insurance plans as people with known medical conditions that will require treatment with certainty, the costs of which are virtually guaranteed to be more than the premiums that insurance companies could charge Suppose we have a population of patients with different health profiles, so that the cost of future treatment X is uniformly distributed on the interval [0, 1000], X˜ ∼ U [0, 1000]. Suppose that we have an insurance company that is bound to offer the same plan to all customers who wish to buy it and cannot deny coverage based on pre-existing conditions. The market for insurance is competitive, so that the insurance company must set its premium equal to the expected future payout. P = E[X˜] Another key provision of the ACA was the “individual mandate,” which required…The deterrence hypothesis, outlined in the abstract and introduction of Gneezy and Rustichini's paper, suggests that: