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- I need some help drawing the curve for p1+p2+p3In some circumstances, individuals reproduce better when the population size is large, and fail to reproduce when the population size is small (the Allee effect introduced in Exercise 46). Suppose that per capita production is an increasing linear function with λ(0) =−2 and a slope of 0.01. Find λ(b) and the differential equation for b. Is b(t) increasing when b = 100? Is b(t) increasing when b = 300?Kusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L 0.6 while its (hourly) cost function is C=20L+80K. Furthermore, Kusho must produce q0=400 computer chips per hour. a. Which levels of L and K satisfy the first-order conditions for the constrained minimisation of Kusho’s cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrangemultiplier b. Show that MRTS=w at the constrained cost minimising levels of L and K obtained above
- As a manager of a small software retailing company, you are concerned with projected profit next year. While profit can be determined as the difference between sales and maintenance cost, or in symbols, P = S - M, where P is profit, S is sales, and M is maintenance cost including technical support. It is argues that when sales goes up so does maintenance cost because the cost of technical support will go up. Further, it is measured that the correlation between S and M is 0.8. Now given the figure that sales next year is expected to be $300 thousand with standard deviation of $4 thousand and maintenance cost is expected to be $150 thousand with standard deviation of $6 thousand, what would be the expected profit and its standard deviation you will include in your report?Is the cobb-douglas function concave if a1 +a2 = 1 whenDefine time preferences for consumption
- The demand equation for a product for a product brand of mackerel is given by the equation Qx=50-7Px+0.002I+12Py Where Qx=monthly consumption per family in cartons Px=price per carton of makerel=GHC 2.00 I=median annual family income=GHC20,000 Py=price per carton of competing brand of mackerel=2.5 Required: i.At the stated values of the explanatory variables,calculate the consumption of makerel(cartons). ii.what is the relationship between Good x and Good y? iii.what is the nature of Good x ? iv.Suppose the median annual family income increases to GHC40,000,What will be your new consumptino for Good x? v.Suppose that the price per carton of competing brand increases GHC3.00, What will be your new consumption for Good x?Suppose you have been hired by a research firm trying to understand the market for Widgets (a hypothetical product). Your analysis of the data indicates that the Demand curve for Widgets is estimated to be linear and given by equation Qd = 150 – 3P and the Supply curve for Widgets appears to be linear as well and is estimated as Qs = 2P – 20. Graphically draw these two curves, labeling all relevant points (such as intercepts for each line) on the horizontal and vertical axes.Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is y = 44t + 0.5t2 − t3, 0 ≤ t ≤ 6. (a) Find the critical values of this function. (Assume −∞ < t < ∞. Enter your answers as a comma-separated list.) t = (b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.) t = (c) For which values of t, for 0 ≤ t ≤ 6, is y increasing? (Enter your answer using interval notation.)
- Ceteris paribus, an increase in productivity would be represented by a movement from A) SRAS1 to SRAS2. B) SRAS2 to SRAS1. C) point A to point B. D) point B to point A. Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.John and Peter are two representative consumers/investors who maximize the utility of consumption. John's utility of consumption is characterized as ln(x) + 2ln(y) while Peter puts more weight on the current consumption level and has a utility function of 2ln(x) + ln(y). John has a wealth of ($10, $20) thousand, while Peter has a wealth of ($20, $15) thousand now and next year, respectively. (a) What are the optimal consumption plans forJohn and Peter,respectively,if the interest rate is 5% per annum? (b) If John and Peter are the only investors/consumers, what is the equilibrium interest rate? (c) Further to part (b), how much do they borrow or lend to each other?Suppose that a house loan of $1,000,000 is to be paid off by equal monthly payments of $ d over the course of 30 years. Suppose that the loan accrues interest at a rate of 1%, compounded monthly. Let Yn be the amount of money owed at the beginning of the n-th month; thus, yo = 1,000,000 and the first payment and first interest charge both occur at time n = 1. (a) Show that the causal sequence yn satisfies yn = 1.014n-1 +1,000,0008,-dun-1. (b) Use the 2-transform to solve for yn (c) Set Y360 = 0 in order to solve for d. (d) What is the total sum of payments made over the 30 years?