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- In the least-squares line ý = 5 + 6x, what is the marginal change in ý for each unit change in x?In the least-squares line = 5 + 2x, what is the marginal change in for each unit change in x?Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the supply of labor is N=1000 + 1000w. Find the market clearing real wage rate and level of employment. What happens to the wage rate and employment if wealth rises, reducing the supply of labor to N= 500 + 1000w? As in (a), what is the unemployment rate if real wage is 1 more than the equilibrium wage? (hint: solve the real wage and then add it by 1, then find the difference of quantity of labor supplied and demanded).
- A standard "money demand" function used by macroeconomists has the form In(m) = Bo + B, In(GDP) + B2R, Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that B, = 2.15 and B, = -0.06. %3D What is the expected change in m if GDP increases by 3%? The value of m is expected to V by approximately%. (Round your response to the nearest integer) What is the expected change in m if the interest rate increases from 1% to 9%? The value of m is expected to ▼ by approximately %. (Round your response to the nearest integer)b) If the marginal revenue function for a manufacturer's product is dr = 2000 – 209 – 3q² dq Find the demand function for the manufacturer's product.28. costsin 2t dt
- 2) A production function for a business follows the model P(L, K) = 0.1 L0.4K0.6 over the course of one year, where P represents the total value of all products the company makes, L represents the value of the labor from employees, and K represents the value of all the company's assets (buildings, machines, etc.), where everything is measured in millions of dollars. ap a. Find and ƏL ap ак' , and explain what they represent in this context. b. Evaluate the partial derivatives from part a when (L, K) = (3,4). If this was your business and your values, if you wanted to expand would it be better to expand in workforce (increase L) or expand in assets (increase K)?A standard "money demand" function used by macroeconomists has the form In(m) = fo + B,In(GDP) + 62R, Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that B, = 2.28 and B2 = - 0.09. What is the expected change in m if GDP increases by 1%? The value of m is expected to increase by approximately 2 %. (Round your response to the nearest integer) What is the expected change in m if the interest rate increases from 1% to 6%? The value of m is expected to decrease by approximately 45 %. (Round your response to the nearest integer)1. Benefit Cost analysis.Assume a benefit function B = 60*x^.8 and a cost function C = 4 + 7*x^1.5. The maximum difference between B and C are the net benefits. a) Find the value of x that results in the maximum net benefits. b) Would an increase in the fixed cost of 4 affect the value of x? c) Use a Lagrangian model to find the value of the shadow price, or Lagrangian multiplier, if x cannot exceed 5. What does the multiplier signify?
- In the least-squares line ŷ = 5 − 2x, what is the value of the slope? In the least-squares line ŷ = 5 + 7x, what is the marginal change in ŷ for each unit change in x?The supply function for a product is Ps(q) = (4 + 0.2q)3/2 where q is in thousands of truckloads and ps(q)is indollars per truckload. Market equilibrium occurs at a demand of 60 thousand truckloads. Compute producer’ssurplus.A. $1856 thousand B. $2865 thousand C. $1238 thousand D. $2855thousandSuppose you're going to sell a certain product, and your marketing team has determined that the maximum number of units of the product that can be sold (based on number of households, desirability, and so on) is given by a constant M>0, and that the rate of increase in unit sales will be proportional to the difference between M and the number of units that have currently been sold. Then the cumulative number of units >0, sold for any time t will be given by a function of the form: A. U(t) = Aekt where A is some undetermined constant, and k > 0 is some proportionality constant. B. U(t) = Aekt – M, where A is some undetermined constant, and k > 0 is some proportionality constant. C. U(t) = Ae-kt - M, where A is some undetermined constant, and k > 0 is some proportionality constant. D. U(t) = Ae¯kt + M, where A is some undetermined constant, and k> 0 is some proportionality constant. E. U(t) = Aekt + M, where A is some undetermined constant, and k> 0 is some proportionality constant.