The optimal bundle for the weekly consumption of tea and coffee by Paul is identified from the diagram at point "X" which is the intersecting point of the indifference curve IC2 and the budget line BL. It is assumed that £15 and £28 are the prices of tea and coffee respectively allocated in the budget of Paul which makes the total budget to become £43 (BL). The optimal bundle of weekly consumption of "tea and coffee" determines that for the given budget Paul, it will be most favourable for him if he chose IC2 or point X where he will be able to consume a suitable quantity of both tea and coffee based on his budget.
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b1): Paul would prefer bundle Z over Y, between the bundles Z and Y. A bundle of coffee and tea on a higher indifference curve would provide more satisfaction to Paul. In the mentioned diagram, point Z is on a higher indifference curve than point Y
b2): Bundle Z costs more between bundles Z and Y. Point Z is to the right of the budget line BL, indicating that it represents a bundle of coffee and tea that costs more than Paul's budget can currently afford. This is because the slope of the budget line reflects the relative prices of coffee and tea, which determine the opportunity cost of consuming one good over the other.
c) Labelling the bundle
Figure 1: Placing dots on the diagram for bundles A, B, C and D
c1): Paul prefers A over all of the bundles X, Y and Z which is why the bundle is placed beyond the IC1 as this would project him with maximum satisfaction.
c2): Bundle B is placed on IC3 as X is better than B and B is better than Y residing on the same IC because in bundle B Paul will be more satisfied than in bundle Y.
c3): Bundle C does not exist as the conditions say that Paul can afford bundle C so it must reside on the budget line. Also, Paul prefers Z over C and C over X so bundle C must be below Z. However, X is the optimal bundle on the budget line which is why all conditions cannot get fulfilled.
c4): Paul is prefers X, Y and Z bundles over Z and he cannot afford D as this includes more tea. Therefore, the budget line requires increasing as the price of tea increases and it is at the right side of the new budget line depicting that it is costing more.
d) Price of the cup of coffee
The price per cup of tea is £1.40 and the total budget allocated for tea consumption is £15. The cost of total coffee consumption is £28 and the total budget for Paul is £43. The weekly budget for the hot drinks that are enjoyed by Paul is estimated as the total values of the costs of tea and coffee as mentioned in the diagram which were £15 and £28 are the prices of tea and coffee respectively, so the budget is £43 (£15 + £28). Therefore, the price for a cup of coffee is £43 divided by £28 which is resulting in £1.54. Hence, Paul has to pay £1.54 for each cup of coffee consumed by him.
e) Identification of the chain of events
In this case, Paul has changed the optimal bundle from bundle X to bundle Y although he insists his preference for ordering the bundles has remained the same. It is identified that had been a chain of events that could have resulted in this change in Paul's optimal bundle which had changed due to this shift. Firstly, Paul is now consuming more quantities of tea compared to coffee, as point Y is placed upward the budget line BL. Secondly, the budget spent by Paul had lowered as well as it was on point X, also the IC3 is below the budget line.
Question 2
a) Completion of the table
A small-scale manufacturer of high-end coffee machines is selling the same on a perfectly competitive market at the market price of £1,000 per machine. The following table indicates how much it costs you to produce certain number of coffee machines per month.
In this case, based on the numerical of the table the quantities are projected along with the total costs of the coffee machines. Marginal cost is calculated as the change in total cost taking place with the increasing number of each unit. The variable costs for the machines had been estimated assuming that 200 is the fixed cost as this was the cost incurred when the output quantity was 0. Therefore, the excess of total cost minus the fixed cost of 200 is resulting to be the variable cost. The "average variable cost" is estimated by variable cost divided by output (Attanasio et al. 2020). The marginal revenue had been estimated based on the formula of changes in total revenue due to per-unit change where total revenue is "total cost multiplied by quantity". Estimation of average revenue is resulting as "total revenue divided by total output".
b) Optimal output of the coffee machines
Based on the rule it states that the "optimal output rule" when the profit of a business is maximised will be projected at the point where "marginal costs equal marginal revenues" or MR= MC. In this case, at quantity 1, both the "marginal costs and marginal revenues" are an equal value of 500. Therefore, at the production of 1 unit, the manufacturer will experience the optimal output condition.
c) Description of the shape and reason behind the production function
The shape of the production function will be curved downward getting flatter because the quantity is increasing gradually which is caused due to the phenomenon of "diminishing marginal utility" (Lin & Peng, 2019).
References
Attanasio, O., Cattan, S., Fitzsimons, E., Meghir, C., & Rubio-Codina, M. (2020). Estimating the production function for human capital: results from a randomized controlled trial in Colombia. American Economic Review, 110(1), 48-85. Retrieved on: 7.02.22, from: https://www.nber.org/system/files/working_papers/w20965/w20965.pdf
Lin, C. C., & Peng, S. S. (2019). The role of diminishing marginal utility in the ordinal and cardinal utility theories. Australian Economic Papers, 58(3), 233-246. Retrieved on: 7.02.22, from: https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-8454.12151
