Given C = 89 + 0.6Y, I = 100-150i, G = 20, Ms = 275, MD = 0.1Y+ 240-250i, derive the IS and LM equations as I = f(Y), and solve for i and Y at equilibrium.
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- While working with the sales manager of your firm, you have estimated the following model of sales volume as a function of monthly household income: In(Q) = 3.418 + 1.212 ln(1) where Q is monthly sales volume, I is monthly household income (in $000). What does the model predict sales volume when income is $4000 per month? 708134 163.73 It cannot be determined without more information None of the aboveAnalysis 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.)Please solve this question and kindly use this formula F=P(1+in)
- QUESTION TWO¶ A. Use Hessian Matrix to classify the stationary point of the function. π = 500₁ - 2Q1 +9502-40% - 30102¶ T B. Write down the associated Hessian matrix and hence determine the nature of the stationary point of this function. Z = X² + y² - 2X4Y+ 15(1.4) Consider the following IS-LM model: I Y=C+I+G C=100+0.4(Y-T) I= 150 +0.2Y - 4,000r r = 0.01 with G = 200 and T = 100. (a) Derive the IS curve and draw it in an appropriate diagram. (b) Calculate the equilibrium values of Y, C, I and r. (c) What is the impact of decreasing government spending to G' = 180 in terms of the new equilibrium value Y"? (d) Suppose the central bank decides it wants to counteract the restrictive fiscal policy. What exactly (i.e. we look for graphical and numerical answers) can the central bank do in order to keep equilibrium output at the value obtained for Y in (b)?A firm's production is Q= 60L-0.02L² Where Q denotes output and L denotes the size of the workforce, calculate the value of MPL when (i) L = 10 (ii) L = 100
- C. Suppose your neighbor is a physics major who also races motorcycles, and she tells you that horsepower can be expressed in terms of the following equation: H = MDA/S where M=mass, D-distance, A=acceleration and S and H are as defined above. Based on this conversation with your neighbor, you decide to change the functional form of the relationship to include 1/H rather than H as an explanatory variable because that's the appropriate theoretical relationship between the two variables. Estimate the above equation, substituting 1/H for H. Which of the two models do you prefer and why?1. Suppose that an equation for infant mortality is described by the function: - VD (P)1². where i is the infant mortality rate (expressed in per 1,000 children), Y is the gross domestic product (in US dollars), P is the population, and 3 and b are constants. a. Derive a linear (in parameters) equation from the function above with In i as the left Y -hand side variable and In y on the right-hand side. Note that y =, which is the P' GDP per capita. b. Identify the slope and intercept in the derived equation in (a). What could be the relationship between i and y? Provide an economic explanation. c. Derive a formula of the slope parameter in the linear equation in (a) for the interpretation of the changes in the variables. Interpret the resulting equation.Consider the following model for the production of refined oil: MSC = 10+ 0.5Q; MEC = 0.30: MSB = 30-0.3Q; MEB = 0. Based on the model, the MPC function is: MPC 20-0.8Q a. MPC 10+ 0.8Q MPC 10+ 0.2Q b. MPC30-0.6Q C. d.
- With respect to a given product, describe the connection that exists between equalibrium/disequalibrium and prediction. cite an unique exampleGiven Q1 = 150 -3P1 + P2 + P3 Q2 = 180 +P1 - 4P2 + 2P3 Q3 = 200 +2P1 + P2 - 5P3 and TC =Q12 + Q1Q2 +2Q22 + Q2Q3 +Q32 + Q1Q3 Find the inversedemand function P = f(Q) and use Cramer’s rule to solve for thecritical value Q1. (Answer in two decimal places.) Use Cramer’s rule tosolve for the critical value Q2. (Answer in two decimalplaces.) Use Cramer’s rule tosolve for the critical value Q3. (Answer in two decimalplaces.) Calculate the Hessian matrix. What is the value of|H3|? (Answer in two decimal places.) Based on the Hessian, what can you say about the profit? (Answer in one word. )Solve each of the following equations for x x+7=14 5x+4=24 12−4x=−20 Organize each of the following equations to express Pas a function of Q. QQ as a function of P PP as a function of Q Q=25−P Q=12−3P 6Q=14−2P