Question 3: Consider the following equation: 1 1 kt+1 = (1+ n)(1+g) 2+ p (1-a)k;ª How does a rise in n affect kt+1 as a function of k? Use a graph to support your answer. Question 4: Consider the following equation: 1-0 (1+r,) 1 1-0 (1+p)ē +(1+,1) Derive the effect of a change in the interest rate r+1 on household's savings rate, expressed as a function of 0.
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- It is known that the ABC oil company supplies consumers with 150 tons of products per day. The company produces only two types of products - gasoline and diesel fuel. The limiting transformation ratio of diesel fuel relative to gasoline is 0.5. a) Draw a line of the company's monthly production capacity for gasoline and diesel. b) With the advent of new technologies, production increased by 20%, and the availability of gasoline increased by 30%. Explain how the company's new product line differs from the previous one. c) If we put the gasoline production on the X-axis of the graph, what percentage of the slope capacity of the production line is different from the slope ratio of the previous production line?Q: Determine whether the following statemnts are true or false: a) If the firm increases the volume of used resources by 30%, and the volume of production thus increases by 20%, then there is a positive effect of the production scale. b) Average fixed costs decrease as production increases. c) The economic profit usually exceeds the accounting profit.Explain the relationship between these two formulas: Y = C + I + G + EX – IM S = (Y – T – C) + (T – G)
- Constrained Optimization using Lagrange Multiplier: Cost MinimizationA clothing company produces two goods namely pants (P) and sweaters (S) whose combined cost function is C = 6P2 + 10S2 − PS + 30.In a day, the clothing company is limited by a production quota of 34 units of output only. Inequation form: P + S = 341. State the cost minimization problem of the clothing company.2. Set-up the Lagrange equation and determine the quantity of pants (P) and sweaters (S) that the firm should produce daily to minimize cost.3. What is the effect on cost if the company decides to increase the production quota by 1 more unit?Suppose U.S. drivers purchased $50 billion of ExxonMobil-produced gasoline during a recent year, with one-half purchased directly from ExxonMobil-owned gas stations and one-half from independent (or third-party) gas stations. Suppose further that ExxonMobil purchased the oil (which it refined into gasoline) from foreign producers for $20billion and that it receives 60 percent of the sales revenue that independent stations generate from selling ExxonMobil gasoline. In this case, the value added by ExxonMobil to U.S. GDP is $__billion.The demand function for apples is the following. Qn = 10 – Pn + 0.2Y +0.5 Pc – 2Ps + 0.2A Where: Qn = annual sales of apples (millions of kilos) Pn = price of apples (£1 per kilo) Y = disposable income in the UK £trillions (£10 trillions) Pc = price of a pies £ per kilo (£2 per kilo) Ps = price of pear (£2 per kilo) A = advertising measured in hundreds of thousands of £5 (use as 5 in your calculations) What is the own price elasticity of demand and what kind of product apple is? a. -1/9, inelastic. b. 1/9, inelastic. c. -2, inelastic. d. -0.5, elastic. e. All the other answers are wrong.
- Suppose that a coffee producing firm estimated the following regression of thedemand for its brand of coffee:Qc = 1.5 − 3.0Pc + 0.8Y + 2.0Pb − 0.6PS +1.2 Awhere Qc = sales of coffee brand C, in dollarsper pound Pc = price of coffee brand C,in dollars per poundY = personal disposable income, in millions of dollars per yearPb = price of the competitive brand of coffee, in dollarsper pound Ps = price of sugar, in dollars per poundA = advertising expenditures for coffee brand C, in hundreds of thousands ofdollars per year.Suppose also that this year, Pc = $2, Y = $2.5, Pb = $1.80,Ps = $1 and A =$1.a. Interpret the results of the estimated demand.b. Compute point price elasticity of demand for the firm’s brand of coffeewith respect to its price.c. Compute the cross-price elasticity of demand for coffee with respect to theprice of competitive coffee brand b.d. At the current price level, would it be viable for the firm to increase the pricelevel of its brand of coffee? Support your answer.…A firm keeps a record of sales and prices over the past seven months, resulting in the following table: Price (ZMW/ton) Sales (tons) Nov. 1985 7.5 84.5 Dec. 8.0 82.0 Jan. 1986 8.0 84.0 Feb. 7.2 92.0 March 7.0 95.0 April 8.0 92.0 May 8.5 91.5 Use these observations to estimate demand as a linear function of both price and time. Further, utilise this function to estimate demand for the following month, on the assumption that: (a) price remains unchanged, (b) price increases to ZMW9/ton. Hence estimate the price elasticity of demand between these prices and find the price which would maximise sales revenue. Given the nature of the observations, comment on any difficulties in interpreting your results for decision-making purposes.The demand function for apples is the following. Qn = 10 – Pn + 0.2Y +0.5 Pc – 2Ps + 0.2A Where: Qn = annual sales of apples (millions of kilos) Pn = price of apples (£1 per kilo) Y = disposable income in the UK £trillions (£10 trillions) Pc = price of a pies £ per kilo (£2 per kilo) Ps = price of pear (£2 per kilo) A = advertising measured in hundreds of thousands of £5 (use as 5 in your calculations) Q. How much will the demanded quantity change if the price of apples increases to 1.5? a. It will decrease by 0.4 million kilos. b. It will decrease by 0.5 million kilos. c. It will increase by 2 million kilos. d. It will increase by 0.5 million kilos. e. All the other answers are wrong.
- The demand function for apples is the following. Qn = 10 – Pn + 0.2Y +0.5 Pc – 2Ps + 0.2A Where: Qn = annual sales of apples (millions of kilos) Pn = price of apples (£1 per kilo) Y = disposable income in the UK £trillions (£10 trillions) Pc = price of a pies £ per kilo (£2 per kilo) Ps = price of pear (£2 per kilo) A = advertising measured in hundreds of thousands of £5 (use as 5 in your calculations) What direction should the apple producers move the price if they wanted to maximize their revenue? a. There is not enough information. b. Don't change the price. c. Cut the price. d. Raise the price.Analysis 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.)Suppose an economy produces only 2 products that will also be used for directconsumption, as per the article at the end of the exam: chicken wings and donuts. Inthe second quarter of 2021 (the base period), 180,000 pounds of chicken wings wereproduced, at a value of $3.50 per pound, while in the second quarter of 2022,production of chicken wings increased to 200,000 pounds, at a value of $3.75 perpound. In the second quarter of 2021 (the base period), 85,000 donuts were producedat a value of $0.85 per donut, while in the second quarter of 2022, donut productionincreased to 100,000 donuts, each at a value of $0.95 per donut. The population inthis economy is 1000 individuals in 2022, while the number of hours worked in 2022is 5000. Also, the quantities that were produced in 2021 represent the quantities thatwere purchased by the typical household, meaning that everything that was producedwas sold.d. Solve for the amount of labor productivity in the second quarter of 2022.e. Solve for the…
