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y = Xß + u where y is nx1, x is nxk, and u is nx1 such that ulx-N(0,0²). Write y = 9+, where 9 = Xß is the least squares predicted value.
a. Show that (B-B) = Au and a = Mu, what is your A and M?
b. Show that y = the mean of the predicted values c. Show that X'û = 0,9'a = 0
d. Derive R² for the model where the first column of X has a constant.
Term for businesses do not maximize output from the given inputs
The Hull Petroleum Company and Inverted V are retail gasoline franchises that compete in a local market to sell gasoline to consumers. Hull and Inverted V are located across the street from each other and can observe the prices posted on each other’s marquees. Demand for gasoline in this market is Q = 90-12P, and both franchises obtain gasoline from their supplier at $3.00 per gallon. On the day that both franchises opened for business, each owner was observed changing the price of gasoline advertised on its marquee more than 10 times; the owner of Hull lowered its price to slightly undercut Inverted V’s price, and the owner of Inverted V lowered its advertised price to beat Hull’s price. Since then, prices appear to have stabilized. Under current conditions, how many gallons of gasoline are sold in the market, and at what price?
Gallons sold: ??
Price $: ??
multiple choice:
a.Price will go down.
b.Price will not change.
c.Price will go up.
Y=A(0.025k-0.5N)N
A=2\3
K=2000
N=-18+(18/5)w
5-c=200+(2/3)(y-T)-300r
6-T=-75+(1/4)Y
I=100-100r
G=100
L=0.5Y-200i
M=6300
π=0.10
What are the values of C, I, L and N
what is the term for when businesses prouduce goods and services that consumers do not want
A principal outsources a work to an agent to deliver y units of output within one month.
(a) Suppose effort is observable. How can the contract be designed so that the agent can be outsourced the first-best level of output?
(b) Now suppose that effort is not observable. Suppose that the agent is risk-averse. Characterize
the contract in this case, clearly
Economics
- If the !"! > 𝑤 holds at T= L for the person i , and !"! < 𝑤 holds at T= L !"" !""
- for the person j what you can conclude about the level of market wage for person i and j . Discuss about their labor force participation rates? (5 points) (T: Number of hours available, L: Number of hours spent for leisure)
Q4. What is crowding-out effect? Explain [2 marks]
Q5. a. What is Phillips curve? Draw the short-run Phillips curve and the long-run Phillips curve. Explain why they are different. <b>[2 marks]
b. Suppose the economy is in a long-run equilibrium. Suppose a wave of business pessimism reduces aggregate demand. Show the effect of this shock on your diagram from part (a). If the RBI undertakes expansionary/contractionary monetary policy, can it return the economy to its original inflation rate and original unemployment rate? (b) What is sacrifice ratio? [5 marks]
A primitive economy depends upon imports M=M(t) to sustain its recently acquired technology. Exports X=X(t) are a fraction of the output Y=Y(t), i.e. X=aY (0<a<1). And output is thought to grow according to the law dy/dt-bM (0<b<1). Current debt satisfies dD/dt=rD+M-X where r is the constant interest rate. Creditors have in mind to allow debt growth to be exactly balanced by export growth, i.e. dD/dt=dx/dt. Find a differential equation for D by eliminating M, X, and Y and hence determine the behaviour of debt. What initial dept to output ratio Do/Yo allows steady state debt? [Hint: D(t)-Do-X(t)-X=X-aY₁ Do and Xo are the initial values]
What will be the rate of interest if money supply increase
