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- In the least-squares line ŷ = 5 + 6x, what is the marginal change in ŷ 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?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)
- 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).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.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)?
- 28. costsin 2t dt1. 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?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)
- 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. $2855thousandIn the least-squares line ŷ = 5 − 3x, what is the value of the slope? In the least-squares line ŷ = 5 + 9x, what is the marginal change in ŷ for each unit change in x?A company has two plants that produce the same lawn mower. If x, and x, are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by R = 800x1 + 800x, - 5x,? – 10x,x2 - 5x,?. When x, = 7 and x2 4, find the following. ƏR (a) Find the marginal revenue for plant 1, Ixe ƏR (b) Find the marginal revenue for plant 2,