Assignment
You may work in teams of no more than 5 students in your registered section - this means you are NOT to share answers across teams (or across sections). One hard copy per team must be handed in. It is recommended that you keep a copy for your records. Please put your names and id's on the top of the first page. You may handwrite-(all or part)-but it must be legible.
For any of the following questions that ask for a particular number show your work. Do not just state facts you might know about certain relationships.
1. In the dataset posted on Canvas you are given 48 observations on Quantity Demanded of Soda, Price of a six pack (in $) and temperature (degrees). Each row of data corresponds to a different market.
a. Perform a regression of Quantity Demanded on Price and Temperature. Recall, the instructions to do regression using Excel are in a word doc under the chapter 4 module.
Attach the regression output to your take home. Write down the equation for the sample regression equation using the coefficients from your regression output. Interpret the numerical coefficients of each of the X variables (discuss not just the sign but also the size of the coefficient).
b. Perform t tests of statistical significance for each of the X variables and interpret those t-tests in terms of the actual variables in the model) - do not just state statistically significant, or insignificant.
c. Assuming the average price and average temperature (they are listed in the last row of the dataset) calculate the own price elasticity of demand,Ep and the temperature elasticity of demand, Etemp.
d. Suppose this firm was to set the same price for its six packs of soda in each of its markets. What would be the revenue maximizing price? How many units of the good would the firm sell at the revenue maximizing price? What would the own price elasticity of demand be at this price?
e. Suppose that the average temperature is expected to increase by 5% this year. What would be the forecasted percentage change in demand?
2. In the article that follows concerning the market for diamonds, there are described factors that affect both supply and demand. Use the appropriate model (graphical analysis) to describe how the factors mentioned would be expected to affect both price and quantity of diamonds. You should also explain in words what is going on in your graphs. Please draw a separate graph for each of the effects.
World diamond supply to peak in 2017,/ De Beers chief executive says
As stones become harder and more costly to extract, very little new supply is expected until 2020
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Global supply of diamonds will peak in 2017 and plateau in 2019, as the world's largest miner and trader of the precious stone reins in production to weather waning demand for jewellery and rising production costs.
But as more rough stones lie in ever deeper mines, the cost of extracting them is increasing, said Bruce Cleaver, chief executive of De Beers Group since July, in an interview with the South China Morning Post.
"What we see is a slow decline in supply, as mines get deeper," said Cleaver, who was in charge of the company's strategy and business development before taking up the post to head the former near monopoly of global diamond trade.
"Between now and 2020 there is very little supply even if all the new projects come online."
The company, owned by Anglo American, which suffered from dwindling diamond prices and rising inventories in a tumultuous 2015, has seen consumer demand growth for diamonds slow in China, at a time when cost pressures are mounting for diamond producers given the challenges now faced in extraction.
De Beers, and its Russian rival Alrosa PJSC, both cut their output in response to last year's downturn. The dominant player has already closed some mines in Canada and Botswana.
"We reduced our production around the world to match demand. At the end of last year we also increased our advertising spend," Cleaver said.
"We are comfortable with the level of production we have for now."
Cleaver noted most of De Beers' new diamond production coming on stream is not going to be from exploration of new mines but from expansion or prolonging of life of existing mines.
De Beers curbed its rough diamond production for the first half of the year by 15 per cent to 13.3 million carats from a year earlier, and maintained its annual mining guidance between 26 million and 28 million, down from 28.7 million last year.
While acknowledging an overhang of global political economic uncertainties, Cleaver said he had seen signs of improvement in the industry's midstream business, essentially dealers and polishers who had held back purchases last year under persistently tight lending terms.
"We find the actions we took last year - producing a bit less and spending more on marketing - have returned the midstream to more normal conditions. They are in a better shape compared with six to 12 months ago," he said.
An imminent pickup in sales is evident in an 8 per cent increase in first half revenuesto US$3.27 billion, while its earnings before interest and taxes also gained 2 per cent to US$585 million, which the company attributed to increasing rough stone demand and operating cost control.
Despite the stabilisation in 2016, the Johannesburg-based firm highlighted in its annual Diamond Insight report that "volatility in the diamond sector is not a short-term phenomenon, but the new normal".
Millennials are an important cohort in the diamond market, and that trend is absolutely in China. For very aspirational purchases in China, brand is very important
BRUCE CLEAVER, CHIEF EXECUTIVE, DE BEERS GROUP
Still, Cleaver is "cautiously optimistic" of long-term demand, as a generation of millennials - those born during the 1980s, reaching adulthood during the 2000s - from China and India are likely to become the main customers as they are financially able to afford diamonds.
"Millennials are an important cohort in the diamond market, and that trend is absolutely in China," he said. "For very aspirational purchases in China, brand is very important."
Self purchases, but not only "a man buying it for a woman", are also poised to be more prevalent, according to a recent De Beers poll of 75,000 millennials on diamond consumption.
"Millennials like things that are easier to be identified, more individualised and there are going to be the challenges for the retailers about how they are changing their designs," Cleaver said.
He stressed that the Chinese desire for luxury gemstones will continue to grow in spite of a lacklustre economy and relatively subdued income growth.
China is already De Beers' second biggest market after the US, with demand from the mainland doubling its share to 14 per cent in 2015 within eight years.
Chinese consumers' recent shift to more affordable alternatives, as well as more exclusive and niche labels following their earlier sophistication in tastes, has meant continued gloom for some prominent luxury retailers such as Prada, which reported a steep 24 per cent plunge in its first half net profits this year.
However, De Beers has said it will ramp up its sales efforts in China's second and third-tier cities, where the huge population and swelling middle classes still bring growth opportunities.
"I would be surprised if you see continuous double-digit growth in diamond demand in China, but the size of the single-digit growth is still quite positive," said Cleaver, adding that there was also "a slight shift towards [diamonds] slightly lower in quality" among Chinese buyers.
While the region's largest jewellers led by Chow Tai Fook rushed to shut stores in the wake of battered earnings and tepid retail sentiment, De Beers plans to relaunch its Forevermark diamond brand in China by the end of the year, with television marketing campaigns lining up for the coming Lunar New Year.
"There are a lot of volatilities, but a lot of demand," added Cleaver.
The world's No 1 diamond producer is also urging miners to invest more in technology, as a higher share of diamond production is poised to come from mines which are costlier and more complex to operate.
"You can't just sit on the increasing costs and do nothing," he said.
This article appeared in the South China Morning Post print edition as: Diamond supply to peak next year, says de Beers chief business-article-page
3. A price-setting firm faces the following estimated demand and average variable cost functions:
Qd = 800,000 - 2,000 P + 0.7 M + 4,000 PR
AVC = 500 - 0.03 Q + 0.000001 Q2
where Qd is the quantity demanded, P is price, M is income, and PR is the price of a related good. The firm expects income to be $40,000 and PR to be $53. Total fixed cost is $2,600,000.
a. Find the profit maximizing output and price for this price setting firm. Calculate the own price elasticity of demand at this price and quantity. Show all your work.
b. Should this firm produce at the profit maximizing output or should it shut down? Explain.
c. Draw the graph for this price setting firm, indicating the profit maximizing output and price. Include all relevant curves and clearly label them. If there are profits (or losses) label the box.
d. Depict what would happen in the graph if for example M dropped. What would happen to price, to quantity? ( You don't need calculations for this).
Attachment:- Data-Set.rar