Assume that demand for a commodity is represented by the equation P = 20 – 0.6 Q d, and supply by the equation P = 10 + 0.2 Qs where Qd and Q s are quantity demanded and quantity supplied, respectively, and P is the Price. Use the equilibrium condition Qs = Qd

1: Solve the equations to determine equilibrium price.

2: Now determine equilibrium quantity.

3: Graph the two equations to substantiate your answers and label these two graphs as D1 and S1.

4: Furthermore; using demand and supply show what happen to equilibrium price and quantity if eating this product causes cardiac problem.

Solow Growth Model

a. Assume the production function is y = f(k) = 5 ∗ √?. That is for a given level of the capital-labor ratio, k, output, y, is five times the square-root of k. Assume n, the rate of population growth, is 0.02 and d, the rate of depreciation is 0.03. Assume the savings rate, s, is 0.10. Calculate the steady state levels of output, y*, and the capital-labor ratio, k* for the Solow Growth Model with no technological progress.

b. Assume the savings rate doubles to s= 0.2, but everything else from part a is the same. Find the new k* and y*.

You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution.

1. Expected Return for Stock X and Stock Y.
2. Standard Deviation for Stock X and Stock Y
3. Would you invest in Stock X or Stock Y? Explain.

Consider a Solow economy with the following production function

F(K,N) = zK^(1/3)N^(2/3)

and parameters d = 0.05, s = 0.2, N0 = 100 and z = 1.0. Suppose K = 300 in period 0 and the

unit period is one year. In contrast to the standard Solow model, we assume that the population

growth rate n is no longer exogenous but rather endogenous and determined by

(1 + n) = N’/N = g(C/N) = (C/N)^3 as it is the case in the Malthusian model.

1) Determine the dynamics for the per worker capital (k). This is the first question in the problem

At a grocery store eggs come in cartons that hold a dozen eggs. Experience indicated that 66.5% of the cartons have no broken eggs, 27.2% have one broken egg, 6.1& have 2 broken eggs, and 0.2% have 3 broken eggs, and the percentage of cartons with 4 or more broken eggs is negligible.

Using baye's rule or law of total probability:

1. an egg is selected at random from a carton. what is the probability that the egg is broken?

2. an egg selected at random from a carton is found to be broken, what is the probability that it came from a carton with to broken eggs?

The flywheel of an old steam engine is a solid homogeneous metal disk of mass M = 112 kg and radius R = 80 cm. The engine rotates the wheel at 520 rpm. In an emergency, to bring the engine to a stop, the flywheel is disengaged from the engine and a brake pad is applied at the edge to provide a radially inward force F = 125 N. If the coefficient of kinetic friction between the pad and the flywheel is μk = 0.2.

How many revolutions does the flywheel make before coming to rest?

How long does it take for the flywheel to come to rest?

Calculate the work done by the torque during this time.

Archie has to go to school this morning for an important test, but he woke up late. He can either take the bus or take his unreliable car. If he takes the car, Archie knows from experience that he will make it to school without breaking down with probability 0.2. However, the bus to school runs late 65% of the time. Archie decides to choose between these options by tossing a coin. Suppose that Archie does, in fact, make it to the test on time. What is the probability that he took his car? Round your answer to two decimal places.

An enzyme acts as a catalyst in the fermentation of A to form product R. An aqueous feed stream containing the enzyme and compound A flows into a CSTR at 25 L/min, and the initial concentration of A is 2 mol*L^-1 . Determine the volume of the CSTR (in Liters, expressed to the nearest integer ) needed to achieve 98% conversion of reactant A. You may assume that the enzyme concentration and volumetric flowrates are constant. The maximum rate of destruction of the substrate is 0.4 mol/(L min). When the substrate concentration is 0.5 mol/L, the rate of destruction of the substrate is 0.2 mol/(L min), i.e. half of the maximum rate.

1. The ordinates of a 6- hr unit hydrograph are given below. A storm had three successive 6 – hr intervals of rainfall magnitude of 3, 5, and 4 cm respectively. Assuming a Φ- index of 0.2 cm/hr and a base flow of 30 m³/s, determine the resulting hydrograph of flow (total flow).

The following data are monthly sales of jeans at a local department store. The buyer would like to forecast sales of jeans for the next month, July.

(a) Forecast sales of jeans for March through June using the naïve method, a two-period moving average, and exponential smoothing with an ? = 0.2. (Hint: Use naïve to start the exponential smoothing process.)
(b) Compare the forecasts using MAD and decide which is best.
(c) Using your method of choice, make a forecast for the month of July.