Read more: Sections 8. Mathematics for economists: An introductory textbook , 4th ed. Manchester: Manchester University Press. We now illustrate the principles of the previous section with specific production and utility functions. We use a and b rather than and because will be used in the production function. Also, as before, we may write this production function in terms of hours of free time t , since. Doing this, and assuming for simplicity that , we see that:. The previous section gives us two ways of solving this problem: we may either use the substitution method or apply the formula.
We will demonstrate both, and confirm that they give us the same answer. We know that the solution to the problem must satisfy this condition, so we calculate the MRT from the feasible frontier, and the MRS from the utility function, and equate the two. As we saw in Leibniz 3. Using the equation above for the frontier:. Also, we showed in Leibniz 3. The marginal utilities are found by differentiating the utility function:. Solving this equation for t , we see that , where.
These are the values of t and y that give Alexei the highest utility he can achieve within the feasible set. The method consists of substituting the constraint into the objective function to make it a function of just one variable and maximizing that function. Substituting the constraint into the utility function gives us an expression for utility as a function of t alone:. As in the general analysis of the previous section, this expresses the net effect on utility of an increase in t as the result of a positive direct effect and the negative effect of a lower exam grade.
Cycling around our sunny island is a great way to get your dose of Vitamin D and enjoy the green spaces that dot our city. Singapore boasts a well-connected network of cycling paths , and you can rent shared bicycles from licensed operators. You can find guidelines for cycling in Singapore here. If you need assistance or have any queries, drop by one of any of the seven Singapore Visitor Centres. The visitor centres boast a range of helpful services and information. Find Out More. Getting Around Singapore Singapore's public transport system is fast and efficient, and will whizz you to memorable attractions without fuss.
By train. Food and Drink in the network. Can I eat and drink in trains and stations? Dedicated nursing rooms are available at the following interchanges: 1. Choa Chu Kang Bus Interchange 2.
Woodlands Temporary Bus Interchange 3. Bukit Panjang Integrated Transport Hub 4. Yishun Integrated Transport Hub. Photography and filming of video within SMRT premises. Aircon in Trains. What is the temperature setting of the aircon in SMRT trains?
The temperatures are pre-set. Foldable Bikes in Trains. This is to prevent the devices from being a tripping hazard for other commuters.
Track Maintenance. A Rail Grinding Vehicle grinds track surface and helps reduce noise from train operations Our maintenance staff inspects the tracks daily to check for track defects.
Track defects can also lead to noise, so our staff inspects the tracks everyday. To do this more efficiently, we invested in a high-tech automatic track inspection system called Rail Vision, which allows us to continuously monitor track conditions, even during train operating hours. SMRT has worked with the Land Transport Authority to establish a monitoring system to measure the noise generated by trains at selected locations close to major residential estates.
The measurements are taken every three months. With the results, we can identify locations where the noise levels are close to the guidelines set, and prioritise preventive maintenance works at these locations to ensure these guidelines are not breached.
Follow Us. A Rail Grinding Vehicle grinds track surface and helps reduce noise from train operations.
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